tag:blogger.com,1999:blog-81857105604729738542024-03-13T23:38:47.833+07:00Fisika SiswaMembudayakan Kembali Membaca, Membudayakan Kembali MenulisUnknownnoreply@blogger.comBlogger1787125tag:blogger.com,1999:blog-8185710560472973854.post-22759501134090073862024-03-05T21:31:00.007+07:002024-03-05T21:33:36.820+07:00Dinamika Gerak Lurus<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEinnGBDjAHBbXBQxXIt149P_vfEb9Q3q4l6JxV7X_rkZ4-01F9g48r8qexRYk4Va2UPm8aWamTIF5blmw5yyc-4_je0UvZKVpsx9JdxHlaFVXWacjKXjRMx6V-7G7r6wKlu90raS3TfLT6XPefGVWJT0Ea4EqbpIaBQNLMPJwUM6ZQr8IPAzTLKjOfzFy8" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1080" data-original-width="1920" src="https://blogger.googleusercontent.com/img/a/AVvXsEinnGBDjAHBbXBQxXIt149P_vfEb9Q3q4l6JxV7X_rkZ4-01F9g48r8qexRYk4Va2UPm8aWamTIF5blmw5yyc-4_je0UvZKVpsx9JdxHlaFVXWacjKXjRMx6V-7G7r6wKlu90raS3TfLT6XPefGVWJT0Ea4EqbpIaBQNLMPJwUM6ZQr8IPAzTLKjOfzFy8=s16000" /></a></div><br /><p></p>
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overflow: hidden; padding-left: 11px; padding-right: 11px; text-overflow: ellipsis; text-wrap: nowrap; transition-duration: 0.1s; transition-property: background-color, color, border-color, box-shadow; user-select: none;"><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive" style="background-image: url("/w/load.php?modules=skins.vector.icons&image=language&variant=progressive&format=original&lang=id&skin=vector-2022&version=zliox"); background-position: center center; background-repeat: no-repeat; background-size: max(1.25em, 20px); display: inline-block; font-size: 14px; height: 1.25em; margin-right: 6px; min-height: 20px; min-width: 20px; vertical-align: text-bottom; width: 1.25em;"></span><span class="vector-dropdown-label-text" style="font-size: 0.875em;">6 bahasa</span></label></div></header><div class="vector-page-toolbar" style="background-color: white; color: #202122; font-family: sans-serif; font-size: 16px; grid-area: toolbar / toolbar / toolbar / toolbar;"><div class="vector-page-toolbar-container" style="box-shadow: rgb(200, 204, 209) 0px 1px; 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position: relative; z-index: 0;"><div class="vector-body-before-content" style="overflow: hidden;"><div class="mw-indicators" style="float: right; font-size: 0.875em; line-height: 1.6; margin-top: 8px; padding-top: 0.4em; position: relative; z-index: 1;"></div><div class="noprint" id="siteSub" style="font-size: 11.2px; margin-top: 8px;">Dari Wikipedia bahasa Indonesia, ensiklopedia bebas</div></div><div id="contentSub" style="color: #54595d; font-size: 0.875rem; margin: 8px 0px 0px; width: auto;"><div id="mw-content-subtitle"></div></div><div class="mw-body-content" id="mw-content-text" style="margin-top: 16px;"><div class="mw-content-ltr mw-parser-output" dir="ltr" lang="id"><div class="hatnote navigation-not-searchable" role="note" style="font-style: italic; margin-bottom: 0.5em; padding-left: 1.6em;">Halaman ini berisi artikel tentang notasi matematika dari konsep lawas tentang perubahan yang sangat kecil. Untuk penggunaan yang lebih umum, lihat <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Diferensial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Diferensial">Diferensial</a>.</div><p style="margin: 0.5em 0px 1em;">Dalam <a href="https://id.wikipedia.org/wiki/Matematika" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Matematika">matematika</a>, <b>diferensial</b> mengacu pada beberapa notasi/konsep yang saling berhubungan<sup class="reference" id="cite_ref-1" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Diferensial_(matematika)#cite_note-1" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[1]</a></sup> dan berasal dari awal perkembangan ilmu <a href="https://id.wikipedia.org/wiki/Kalkulus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kalkulus">kalkulus</a>. Secara lebih matematis, istilah ini mengacu pada perubahan/selisih yang <a href="https://id.wikipedia.org/wiki/Infinitesimal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Infinitesimal">infinitesimal</a> dan <a href="https://id.wikipedia.org/wiki/Turunan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan">turunan</a> dari fungsi. Istilah ini dipakai dalam berbagai cabang matematika seperti <a href="https://id.wikipedia.org/wiki/Kalkulus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kalkulus">kalkulus</a>, <a href="https://id.wikipedia.org/wiki/Geometri_diferensial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Geometri diferensial">geometri diferensial</a>, <a href="https://id.wikipedia.org/wiki/Geometri_aljabar" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Geometri aljabar">geometri aljabar</a> dan <a href="https://id.wikipedia.org/wiki/Topologi_aljabar" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Topologi aljabar">topologi aljabar</a>.</p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Pendahuluan">Pendahuluan</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Diferensial_(matematika)&veaction=edit&section=1&editintro=Template:Disambig_editintro" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Pendahuluan">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Diferensial_(matematika)&action=edit&section=1&editintro=Template:Disambig_editintro" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Pendahuluan">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><p style="margin: 0.5em 0px 1em;">Istilah <b>diferensial</b> adalah terjemahan dari kata bahasa Inggris <i>differential</i>. Secara informal, kata <i>differential</i> digunakan dalam <a href="https://id.wikipedia.org/wiki/Kalkulus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kalkulus">kalkulus</a> untuk merujuk suatu perubahan yang <a href="https://id.wikipedia.org/wiki/Infinitesimal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Infinitesimal">infinitesimal</a> ("<i>infinitely small</i>", sangat kecil) pada suatu <a href="https://id.wikipedia.org/wiki/Variabel_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Variabel (matematika)">variabel</a>. Sebagai contoh, jika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> adalah suatu variabel, maka besar perubahan/selisih dari nilai <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> sering dinyatakan dengan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \Delta x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi mathvariant="normal">Δ</mi><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \Delta x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3890eb866b6258d7a304fc34c70ee3fb3a81a70" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 3.266ex;" /></span> (dibaca sebagai <i><a href="https://id.wikipedia.org/wiki/Delta_(huruf)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Delta (huruf)">delta</a> <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span></i>). Diferensial <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">dx</span> menyatakan perubahan nilai yang sangat kecil pada variabel <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>. Konsep dari perubahan yang sangat kecil cukup intuitif dan memiliki peran yang sangat penting dalam matematika. Ada beberapa cara berbeda untuk mendefinisikan konsep ini secara matematis.</p><p style="margin: 0.5em 0px 1em;">Penggunaan <a href="https://id.wikipedia.org/wiki/Turunan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan">turunan</a> memungkinkan perubahan infinitesimal suatu variabel dinyatakan sebagai perubahan-perubahan infinitesimal dari variabel-variabel lain. Jika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> adalah fungsi terhadap <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>, maka diferensial <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">dy</span> dari variabel <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> terhubung dengan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">dx</span> lewat persamaan</p><div class="mwe-math-element" style="max-width: 100%; overflow-x: auto;"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; height: 1px; margin-bottom: 0.6em; margin-left: 1.6em !important; margin-right: auto; margin-top: 0.6em; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle dy={\frac {dy}{dx}}\,dx,}" display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mi>�</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi>�</mi><mi>�</mi></mrow><mrow><mi>�</mi><mi>�</mi></mrow></mfrac></mrow><mspace width="thinmathspace"></mspace><mi>�</mi><mi>�</mi><mo>,</mo></mstyle></mrow></semantics></math></div><img alt="{\displaystyle dy={\frac {dy}{dx}}\,dx,}" aria-hidden="true" class="mwe-math-fallback-image-display mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8690f9df1066aadc3c2999e8633a040038558df" style="border: 0px; display: block; height: 5.509ex; margin-bottom: 0.6em; margin-left: 1.6em !important; margin-right: auto !important; margin-top: 0.6em; vertical-align: -2.005ex; width: 12.431ex;" /></div>dengan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\tfrac {dy}{dx}}\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mrow><mi>�</mi><mi>�</mi></mrow><mrow><mi>�</mi><mi>�</mi></mrow></mfrac></mstyle></mrow><mspace width="thinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\tfrac {dy}{dx}}\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d638cbaa3b3e14dfbf4a9ff92e27760b84572e0" style="border: 0px; display: inline-block; height: 4.176ex; vertical-align: -1.338ex; width: 3.023ex;" /></span>menyatakan <a href="https://id.wikipedia.org/wiki/Turunan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan">turunan</a> dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> terhadap <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>. Rumus tersebut merangkum ide intuitif bahwa turunan dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> terhadap <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> adalah <a class="mw-disambig" href="https://id.wikipedia.org/wiki/Limit" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Limit">limit</a> dari rasio <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\tfrac {\Delta y}{\Delta x}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mrow><mi mathvariant="normal">Δ</mi><mi>�</mi></mrow><mrow><mi mathvariant="normal">Δ</mi><mi>�</mi></mrow></mfrac></mstyle></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\tfrac {\Delta y}{\Delta x}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3aa2e28168373c76134102582fee536a643bcf63" style="border: 0px; display: inline-block; height: 4.176ex; vertical-align: -1.338ex; width: 3.145ex;" /></span> saat <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \Delta x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi mathvariant="normal">Δ</mi><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \Delta x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3890eb866b6258d7a304fc34c70ee3fb3a81a70" style="border: 0px; display: inline-block; height: 2.176ex; vertical-align: -0.338ex; width: 3.266ex;" /></span> menjadi infinitesimal. Terdapat beberapa pendekatan untuk mendefinisikan secara matematis konsep diferensial:<p style="margin: 0.5em 0px 1em;"></p><ol style="list-style-image: none; margin: 0.3em 0px 0px 3.2em; padding: 0px;"><li style="margin-bottom: 0.1em;">Diferensial sebagai <a href="https://id.wikipedia.org/wiki/Peta_linear" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Peta linear">pemetaan linear</a>. Cara ini mendasari definisi <a class="new" href="https://id.wikipedia.org/w/index.php?title=Turunan_total&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan total (halaman belum tersedia)">turunan total</a> dan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Turunan_eksterior&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan eksterior (halaman belum tersedia)">turunan eksterior</a> dalam ilmu <a href="https://id.wikipedia.org/wiki/Geometri_diferensial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Geometri diferensial">geometri diferensial</a>.<sup class="reference" id="cite_ref-2" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Diferensial_(matematika)#cite_note-2" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[2]</a></sup></li><li style="margin-bottom: 0.1em;">Diferensial sebagai kelas ekuivalensi <i>germ</i> dari fungsi-fungsi.</li><li style="margin-bottom: 0.1em;">Diferensial sebagai elemen <a class="new" href="https://id.wikipedia.org/w/index.php?title=Nilpoten&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Nilpoten (halaman belum tersedia)">nilpoten</a> dari <a href="https://id.wikipedia.org/wiki/Gelanggang_komutatif" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Gelanggang komutatif">gelanggang komutatif</a>. Pendekatan ini populer dalam <a href="https://id.wikipedia.org/wiki/Geometri_aljabar" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Geometri aljabar">geometri aljabar</a>.<sup class="reference" id="cite_ref-Harris1998_3-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Diferensial_(matematika)#cite_note-Harris1998-3" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[3]</a></sup></li><li style="margin-bottom: 0.1em;">Diferensial dalam <i>smooth model</i> pada teori himpunan.<sup class="reference" id="cite_ref-4" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Diferensial_(matematika)#cite_note-4" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[4]</a></sup></li><li style="margin-bottom: 0.1em;">Diferensial sebagai infinitesimals dalam <a class="new" href="https://id.wikipedia.org/w/index.php?title=Sistem_bilangan_hiperreal&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Sistem bilangan hiperreal (halaman belum tersedia)">sistem bilangan hiper-real</a>, yakni perluasan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Bilangan_real" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan real">bilangan real</a> yang mengandung infinitesimal terbalikkan dan bilangan yang tak hingga besarnya. Cara ini adalah pendekatan analisis non-standar yang dikembangkan oleh <a href="https://id.wikipedia.org/wiki/Abraham_Robinson" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Abraham Robinson">Abraham Robinson</a>.<sup class="reference" id="cite_ref-nonstd_5-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Diferensial_(matematika)#cite_note-nonstd-5" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[5]</a></sup></li></ol><p style="margin: 0.5em 0px 1em;">Pendekatan-pendekatan tersebut sangat berbeda satu sama lainnya. Tetapi mereka semua memiliki ide bersifat <i>kuantitatif</i>, maksudnya tidak hanya berkata diferensial adalah sesuatu yang sangat kecil, tapi <i>juga seberapa</i> kecil dia.</p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Notasi_dasar">Notasi dasar</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Diferensial_(matematika)&veaction=edit&section=2&editintro=Template:Disambig_editintro" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Notasi dasar">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Diferensial_(matematika)&action=edit&section=2&editintro=Template:Disambig_editintro" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Notasi dasar">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;">Karena kata diferensial berkembang dalam beberapa cabang kalkulus, diferensial dapat merujuk konsep "perubahan yang sangat kecil" yang berbeda. Dalam <a href="https://id.wikipedia.org/wiki/Kalkulus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kalkulus">kalkulus</a>, diferensial merujuk pada perubahan akibat mencari aproksimasi linear sebuah <a href="https://id.wikipedia.org/wiki/Fungsi_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi (matematika)">fungsi</a>. Konsep diferensial ini diperumum sebagai <a href="https://id.wikipedia.org/wiki/Diferensial_total" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Diferensial total">diferensial total</a> pada fungsi multivariabel. Dalam pendekatan kalkulus yang tradisional, diferensial (contohnya <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">dx</span>, <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">dy</span>, <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">dt</span>) dianggap sebagai perubahan yang sangat kecil (infinitesimal). Terdapat beberapa cara untuk mendefinisikan secara matematis konsep ini, namun juga cukup untuk mengganggap infinitesimal sebagai bilangan yang <a href="https://id.wikipedia.org/wiki/Nilai_absolut" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Nilai absolut">nilai mutlaknya</a> lebih kecil dari sembarang bilangan real positif; sama seperti tak hingga sebagai bilangan yang lebih besar dari sembarang bilangan real.</p><p style="margin: 0.5em 0px 1em;">Diferensial juga merupakan nama lain dari <a href="https://id.wikipedia.org/wiki/Matriks_Jacobi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Matriks Jacobi">matriks Jacobi</a> dari <a href="https://id.wikipedia.org/wiki/Turunan_parsial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan parsial">turunan parsial</a> fungsi dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} ^{n}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} ^{n}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" style="border: 0px; display: inline-block; height: 2.343ex; margin: 0px; vertical-align: -0.338ex; width: 2.897ex;" /></span> ke <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} ^{m}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} ^{m}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a87a024931038d1858dc22e8a194e5978c3412e" style="border: 0px; display: inline-block; height: 2.343ex; margin: 0px; vertical-align: -0.338ex; width: 3.353ex;" /></span> (khususnya ketika <a href="https://id.wikipedia.org/wiki/Matriks_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Matriks (matematika)">matriks</a> ini dianggap sebagai <a href="https://id.wikipedia.org/wiki/Peta_linear" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Peta linear">peta linear</a>). <a class="new" href="https://id.wikipedia.org/w/index.php?title=Kalkulus_stokastik&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Kalkulus stokastik (halaman belum tersedia)">Kalkulus stokastik</a> memberikan notasi <a class="new" href="https://id.wikipedia.org/w/index.php?title=Diferensial_stokastik&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Diferensial stokastik (halaman belum tersedia)">diferensial stokastik</a> dan kalkulus yang bersesuaian untuk <a href="https://id.wikipedia.org/wiki/Proses_stokastik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Proses stokastik">proses stokastik</a>.</p><p style="margin: 0.5em 0px 1em;">Pada <a href="https://id.wikipedia.org/wiki/Integral_Riemann%E2%80%93Stieltjes" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Integral Riemann–Stieltjes">integral Riemann-Stieltjes</a>, integrator dinyatakan sebagai diferensial dari suatu fungsi. Secara formal, diferensial yang muncul di dalam integral memiliki sifat yang tepat sama dengan diferensial. Hal ini mengartikan rumus <a href="https://id.wikipedia.org/wiki/Integral_substitusi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Integral substitusi">integrasi dengan subtitusi</a> dan <a href="https://id.wikipedia.org/wiki/Integrasi_parsial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Integrasi parsial">integrasi secara parsial</a> pada integral Stieltjes masing-masing berkorespodensi dengan <a href="https://id.wikipedia.org/wiki/Kaidah_rantai" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kaidah rantai">aturan rantai</a> dan <a href="https://id.wikipedia.org/wiki/Kaidah_darab" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kaidah darab">aturan perkalian</a> untuk diferensiasi.</p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Sejarah_dan_penggunaan">Sejarah dan penggunaan</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Diferensial_(matematika)&veaction=edit&section=3&editintro=Template:Disambig_editintro" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Sejarah dan penggunaan">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Diferensial_(matematika)&action=edit&section=3&editintro=Template:Disambig_editintro" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Sejarah dan penggunaan">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><div class="hatnote navigation-not-searchable" role="note" style="font-style: italic; margin-bottom: 0.5em; padding-left: 1.6em;">Lihat pula: <a class="new" href="https://id.wikipedia.org/w/index.php?title=Sejarah_kalkulus&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Sejarah kalkulus (halaman belum tersedia)">Sejarah kalkulus</a></div><p style="margin: 0.5em 0px 1em;">Besaran <a href="https://id.wikipedia.org/wiki/Infinitesimal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Infinitesimal">infinitesimal</a> ("yang sangat kecil") memainkan peranan penting dalam perkembangan kalkulus. <a href="https://id.wikipedia.org/wiki/Archimedes" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Archimedes">Archimedes</a> menggunakan konsep ini, walaupun ia tidak percaya argumentasi menggunakan infinitesimal bersifat tegas (<i>rigor</i>).<sup class="reference" id="cite_ref-6" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Diferensial_(matematika)#cite_note-6" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[6]</a></sup> <a href="https://id.wikipedia.org/wiki/Isaac_Newton" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Isaac Newton">Isaac Newton</a> merujuk konsep ini sebagai <i>fluxions</i>. Tetapi, <a href="https://id.wikipedia.org/wiki/Gottfried_Leibniz" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Gottfried Leibniz">Gottfried Leibniz</a> yang pertama mencetuskan istilah <i>differential</i> untuk besaran infinitesimal dan memperkenalkan notasi untuk mereka, yang masih digunakan saat ini.</p><p style="margin: 0.5em 0px 1em;">Dalam <a href="https://id.wikipedia.org/wiki/Notasi_Leibniz" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Notasi Leibniz">notasi Leibniz</a>, jika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> adalah besaran yang dapat berubah (variabel), maka <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">dx</span> menyatakan perubahan infinitesimal pada variabel <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>. Sehingga, jika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> adalah fungsi terhadap <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>, maka <a href="https://id.wikipedia.org/wiki/Turunan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan">turunan</a> dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> terhadap <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> sering dinyatakan sebagai <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">dy/dx</span>, yang dalam notasi Newton atau <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Joseph-Louis_Lagrange" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Joseph-Louis Lagrange">Lagrange</a> sebagai <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\dot {y}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mover><mi>�</mi><mo>˙</mo></mover></mrow></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\dot {y}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea068ce646833369cccf19795f23613159b5f89f" style="border: 0px; display: inline-block; height: 2.509ex; margin: 0px; vertical-align: -0.671ex; width: 1.302ex;" /></span> atau <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y'}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mo>′</mo></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y'}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a535de94a2183d7130731eab8a83531d7c35c6b" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -0.671ex; width: 1.845ex;" /></span>. Penggunaan diferensial dalam bentuk ini awalnya mengundang banyak kontroversi, sebagai contoh dalam pamflet terkenal <i><a class="new" href="https://id.wikipedia.org/w/index.php?title=The_Analyst&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="The Analyst (halaman belum tersedia)">The Analyst</a></i> oleh uskup Berkeley. Walaupun demikian, notasi ini tetap populer karena menggambarkan ide turunan dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> pada suatu titik <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> sebagai laju sesaat (<a href="https://id.wikipedia.org/wiki/Kemiringan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kemiringan">kemiringan</a> dari <a href="https://id.wikipedia.org/wiki/Garis_singgung" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Garis singgung">garis singgung</a> pada grafik fungsi), yang dapat dihitung dengan mengambil <a class="mw-disambig" href="https://id.wikipedia.org/wiki/Limit" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Limit">limit</a> dari rasio perubahan nilai <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> terhadap perubahan nilai <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>, yakni <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\tfrac {\Delta y}{\Delta x}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mrow><mi mathvariant="normal">Δ</mi><mi>�</mi></mrow><mrow><mi mathvariant="normal">Δ</mi><mi>�</mi></mrow></mfrac></mstyle></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\tfrac {\Delta y}{\Delta x}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3aa2e28168373c76134102582fee536a643bcf63" style="border: 0px; display: inline-block; height: 4.176ex; margin: 0px; vertical-align: -1.338ex; width: 3.145ex;" /></span>, ketika perubahan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> dibuat sekecil mungkin. <a href="https://id.wikipedia.org/wiki/Analisis_dimensi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Analisis dimensi">Analisis dimensi</a> juga berlaku bagi diferensial, sehingga <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">dx</span> memiliki dimensi yang sama dengan variabel <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>.</p><p style="margin: 0.5em 0px 1em;">Kalkulus berkembang menjadi cabang matematika tersendiri pada abad ke-17, walaupun beberapa bagian di dalamnya sudah ada sejak jaman kuno. Pendekatan yang digunakan [contohnya] oleh Newton dan Leibniz ditandai oleh definisi yang tak tegas (tidak matematis) pada istilah seperti diferensial dan "sekecil mungkin". Walaupun argumentasi <a href="https://id.wikipedia.org/wiki/George_Berkeley" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="George Berkeley">uskup Berkeley</a> dalam karya <i><a class="new" href="https://id.wikipedia.org/w/index.php?title=The_Analyst&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="The Analyst (halaman belum tersedia)">The Analyst</a></i> tahun 1734 sebagian besar bersifat teologis, matematikawan modern menyadari validitas argumennya mengenai besaran infinitesimal. Pendekatan kalkulus yang modern tidak memiliki masalah teknis tersebut. Walaupun banyak hal yang tidak tegas, perkembangan kalkulus secara pesat terjadi pada abad ke-17 dan ke-18. Pada abad ke-19, Cauchy dan para matematikawan lain mulai mengembangkan pendekatan <a href="https://id.wikipedia.org/wiki/Limit_fungsi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Limit fungsi">epsilon-delta</a> untuk mendefinisikan kekontinuan, limit, dan turunan, memberikan fondasi matematis untuk kalkulus.</p><p style="margin: 0.5em 0px 1em;">Pada abad ke-20, beberapa konsep baru dalam, sebagai contoh <a href="https://id.wikipedia.org/wiki/Kalkulus_multivariabel" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kalkulus multivariabel">kalkulus multivariabel</a> dan <a href="https://id.wikipedia.org/wiki/Geometri_diferensial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Geometri diferensial">geometri diferensial</a>, terasa memuat maksud dari definisi-definisi lawas, khususnya <i>differential</i>. Saat ini diferensial and infinitesimal menggunakan definisi baru yang lebih tegas dan matematis.</p><p style="margin: 0.5em 0px 1em;">Diferensial juga digunakan dalam notasi <a href="https://id.wikipedia.org/wiki/Integral" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Integral">integral</a> karena suatu integral dapat dianggap sebagai penjumlahan tak hingga banyaknya besaran infinitesimal: Luas daerah di dalam grafik dihasilkan dengan membagi grafik menjadi tak hingga banyaknya persegi panjang yang sangat tipis, dan menjumlahkan semua luas persegi panjang tersebut. Pada ekspresi seperti</p><div class="mwe-math-element" style="max-width: 100%; overflow-x: auto;"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; height: 1px; margin-bottom: 0.6em; margin-left: 1.6em !important; margin-right: auto; margin-top: 0.6em; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \int f(x)\,dx,}" display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>∫</mo><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace><mi>�</mi><mi>�</mi><mo>,</mo></mstyle></mrow></semantics></math></div><img alt="{\displaystyle \int f(x)\,dx,}" aria-hidden="true" class="mwe-math-fallback-image-display mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bbd50daec1c6f3767a42b842a9b203d840e9934" style="border: 0px; display: block; height: 5.676ex; margin-bottom: 0.6em; margin-left: 1.6em !important; margin-right: auto !important; margin-top: 0.6em; vertical-align: -2.338ex; width: 10.578ex;" /></div>Simbol integral (yang merupakan huruf s yang dipanjangkan) menyatakan penjumlahan tak hingga, <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">f(x)</span> menyatakan "tinggi" dari persegi panjang, sedangkan diferensial <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">dx</span> menyatakan lebar persegi panjang yang kecilnya tak hingga.<p style="margin: 0.5em 0px 1em;"></p><div class="reflist reflist-lower-alpha" style="font-size: 12.6px; list-style-type: lower-alpha; margin-bottom: 0.5em;"></div><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Pendekatan">Pendekatan</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Diferensial_(matematika)&veaction=edit&section=4&editintro=Template:Disambig_editintro" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Pendekatan">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Diferensial_(matematika)&action=edit&section=4&editintro=Template:Disambig_editintro" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Pendekatan">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Pendekatan_naif">Pendekatan naif</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Diferensial_(matematika)&veaction=edit&section=5&editintro=Template:Disambig_editintro" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Pendekatan naif">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Diferensial_(matematika)&action=edit&section=5&editintro=Template:Disambig_editintro" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Pendekatan naif">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><table class="sidebar sidebar-collapse nomobile plainlist" style="background: rgb(248, 249, 250); border-collapse: collapse; border: 1px solid rgb(170, 170, 170); clear: right; float: right; font-size: 12.32px; line-height: 1.4em; margin: 0.5em 0px 1em 1em; padding: 0.2em; text-align: center; width: 22em;"><tbody><tr><th class="sidebar-title" style="font-size: 17.864px; line-height: 1.2em; padding: 0.2em 0.8em 0.25em;"><a href="https://id.wikipedia.org/wiki/Kalkulus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kalkulus">Kalkulus</a></th></tr><tr><td class="sidebar-above" style="border-bottom: 1px solid rgb(170, 170, 170); border-top: 1px solid rgb(170, 170, 170); padding: 0.15em 0.25em 0.3em;"><ul style="line-height: inherit; list-style: none none; margin: 0px; padding: 0px;"><li style="margin-bottom: 0px;"><a href="https://id.wikipedia.org/wiki/Teorema_dasar_kalkulus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teorema dasar kalkulus">Teorema dasar</a></li></ul><div class="hlist" style="margin-left: 0em;"><ul style="line-height: inherit; list-style: none none; margin: 0px; padding: 0px;"><li style="display: inline; margin: 0px;"><a href="https://id.wikipedia.org/wiki/Limit_fungsi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Limit fungsi">Limit fungsi</a></li><li style="display: inline; margin: 0px;"><a href="https://id.wikipedia.org/wiki/Fungsi_kontinu" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi kontinu">Kontinuitas</a></li></ul></div><div class="hlist" style="margin-left: 0em;"><ul style="line-height: inherit; list-style: none none; margin: 0px; padding: 0px;"><li style="display: inline; margin: 0px;"><a href="https://id.wikipedia.org/wiki/Teorema_nilai_purata" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teorema nilai purata">Teorema nilai purata</a></li><li style="display: inline; margin: 0px;"><a href="https://id.wikipedia.org/wiki/Teorema_Rolle" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teorema Rolle">Teorema Rolle</a></li></ul></div></td></tr><tr><td class="sidebar-content" style="padding: 0px 0.5em 0.4em;"><div class="sidebar-list mw-collapsible mw-collapsed mw-made-collapsible"><button aria-expanded="false" class="mw-collapsible-toggle mw-collapsible-toggle-default mw-collapsible-toggle-collapsed" style="appearance: none; 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color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kalkulus diferensial">Diferensial</a></span></div></div></td></tr><tr><td class="sidebar-content" style="padding: 0px 0.5em 0.4em;"><div class="sidebar-list mw-collapsible mw-collapsed mw-made-collapsible"><button aria-expanded="false" class="mw-collapsible-toggle mw-collapsible-toggle-default mw-collapsible-toggle-collapsed" style="appearance: none; background-attachment: initial; background-clip: initial; background-image: none; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border-color: initial; border-style: initial; border-width: 0px; cursor: pointer; float: right; font-family: inherit; font-feature-settings: inherit; font-kerning: inherit; font-optical-sizing: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-variation-settings: inherit; font-weight: normal; line-height: inherit; margin: 0px; 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text-decoration-line: none;" title="Kalkulus vektor">Vektor</a></span></div></div></td></tr><tr><td class="sidebar-content" style="padding: 0px 0.5em 0.4em;"><div class="sidebar-list mw-collapsible mw-collapsed mw-made-collapsible"><button aria-expanded="false" class="mw-collapsible-toggle mw-collapsible-toggle-default mw-collapsible-toggle-collapsed" style="appearance: none; background-attachment: initial; background-clip: initial; background-image: none; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border-color: initial; border-style: initial; border-width: 0px; cursor: pointer; float: right; font-family: inherit; font-feature-settings: inherit; font-kerning: inherit; font-optical-sizing: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-variation-settings: inherit; font-weight: normal; line-height: inherit; margin: 0px; padding: 0px 0.2em; text-align: right; user-select: none;" tabindex="0" type="button"><span class="mw-collapsible-text" style="color: #3366cc;">tampil</span></button><div class="sidebar-list-title" style="font-size: 12.936px; font-weight: bold; line-height: 1.6em; padding: 0px 0.4em;"><span style="font-size: 14.2296px;"><a href="https://id.wikipedia.org/wiki/Kalkulus_multivariabel" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kalkulus multivariabel">Multivariabel</a></span></div></div></td></tr><tr><td class="sidebar-content" style="padding: 0px 0.5em 0.4em;"><div class="sidebar-list mw-collapsible mw-collapsed mw-made-collapsible"><button aria-expanded="false" class="mw-collapsible-toggle mw-collapsible-toggle-default mw-collapsible-toggle-collapsed" style="appearance: none; background-attachment: initial; background-clip: initial; background-image: none; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border-color: initial; border-style: initial; border-width: 0px; cursor: pointer; float: right; font-family: inherit; font-feature-settings: inherit; font-kerning: inherit; font-optical-sizing: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-variation-settings: inherit; font-weight: normal; line-height: inherit; margin: 0px; padding: 0px 0.2em; text-align: right; user-select: none;" tabindex="0" type="button"><span class="mw-collapsible-text" style="color: #3366cc;">tampil</span></button><div class="sidebar-list-title" style="font-size: 12.936px; font-weight: bold; line-height: 1.6em; padding: 0px 0.4em;"><span style="font-size: 14.2296px;">Khusus</span></div></div></td></tr><tr><td class="sidebar-navbar" style="font-size: 14.168px; padding: 0px 0.4em 0.4em; text-align: right;"><div class="navbar plainlinks hlist navbar-mini" style="display: inline; font-size: 12.4678px;"><ul style="display: inline-block; line-height: inherit; list-style: none none; margin: 0px; padding: 0px; text-wrap: nowrap;"><li class="nv-lihat" style="display: inline; margin: 0px; word-spacing: -0.125em;"><a href="https://id.wikipedia.org/wiki/Templat:Kalkulus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Templat:Kalkulus"><abbr style="border-bottom: none; cursor: inherit; font-variant-alternates: normal; font-variant-caps: small-caps; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; text-decoration-line: none; text-decoration-style: initial;" title="Lihat templat ini">l</abbr></a></li><li class="nv-bicara" style="display: inline; margin: 0px; word-spacing: -0.125em;"><a href="https://id.wikipedia.org/wiki/Pembicaraan_Templat:Kalkulus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Pembicaraan Templat:Kalkulus"><abbr style="border-bottom: none; cursor: inherit; font-variant-alternates: normal; font-variant-caps: small-caps; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; text-decoration-line: none; text-decoration-style: initial;" title="Diskusikan templat ini">b</abbr></a></li><li class="nv-sunting" style="display: inline; margin: 0px; word-spacing: -0.125em;"><a class="external text" href="https://id.wikipedia.org/w/index.php?title=Templat:Kalkulus&action=edit" style="background: none !important; color: #3366cc; overflow-wrap: break-word; padding: 0px !important; text-decoration-line: none;"><abbr style="border-bottom: none; cursor: inherit; font-variant-alternates: normal; font-variant-caps: small-caps; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; text-decoration-line: none; text-decoration-style: initial;" title="Sunting templat ini">s</abbr></a></li></ul></div></td></tr></tbody></table><p style="margin: 0.5em 0px 1em;">Beberapa buku teks siswa dan mahasiswa menggunakan pendekatan dan nomenklatur lawas yang naif ketimbang memberikan aksioma-aksioma yang tegas, definisi, dan akibat-akibat yang sederhana. Pendekatan dalam <a href="https://id.wikipedia.org/wiki/Kalkulus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kalkulus">kalkulus</a> ini menggunakan istilah <i>diferensial</i> untuk merujuk suatu perubahan yang <a href="https://id.wikipedia.org/wiki/Infinitesimal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Infinitesimal">infinitesimal</a> ("<i>infinitely small</i>", sangat kecil) pada suatu <a href="https://id.wikipedia.org/wiki/Variabel_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Variabel (matematika)">variabel</a>. Sebagai contoh, jika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> adalah suatu variabel, maka besar perubahan/selisih dari nilai <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> sering dinyatakan dengan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \Delta x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi mathvariant="normal">Δ</mi><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \Delta x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3890eb866b6258d7a304fc34c70ee3fb3a81a70" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 3.266ex;" /></span> (dibaca sebagai <i><a href="https://id.wikipedia.org/wiki/Delta_(huruf)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Delta (huruf)">delta</a> <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span></i>). Diferensial <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">dx</span> menyatakan perubahan nilai yang sangat kecil pada variabel <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>. Konsep dari perubahan yang sangat kecil cukup intuitif dan memiliki peran yang sangat penting dalam matematika, kecuali ketika siswa menjadi bingung ketika menyadari ketidakkonsistenan. Ada beberapa cara berbeda untuk mendefinisikan konsep ini secara matematis.</p><p style="margin: 0.5em 0px 1em;">Penggunaan <a href="https://id.wikipedia.org/wiki/Turunan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan">turunan</a> memungkinkan perubahan infinitesimal suatu variabel dinyatakan sebagai perubahan-perubahan infinitesimal dari variabel-variabel lain. Jika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> adalah fungsi terhadap <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>, maka diferensial <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">dy</span> dari variabel <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> terhubung dengan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">dx</span> lewat persamaan</p><div class="mwe-math-element" style="max-width: 100%; overflow-x: auto;"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; height: 1px; margin-bottom: 0.6em; margin-left: 1.6em !important; margin-right: auto; margin-top: 0.6em; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle dy={\frac {dy}{dx}}\,dx,}" display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mi>�</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi>�</mi><mi>�</mi></mrow><mrow><mi>�</mi><mi>�</mi></mrow></mfrac></mrow><mspace width="thinmathspace"></mspace><mi>�</mi><mi>�</mi><mo>,</mo></mstyle></mrow></semantics></math></div><img alt="{\displaystyle dy={\frac {dy}{dx}}\,dx,}" aria-hidden="true" class="mwe-math-fallback-image-display mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8690f9df1066aadc3c2999e8633a040038558df" style="border: 0px; display: block; height: 5.509ex; margin-bottom: 0.6em; margin-left: 1.6em !important; margin-right: auto !important; margin-top: 0.6em; vertical-align: -2.005ex; width: 12.431ex;" /></div>dengan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\tfrac {dy}{dx}}\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mrow><mi>�</mi><mi>�</mi></mrow><mrow><mi>�</mi><mi>�</mi></mrow></mfrac></mstyle></mrow><mspace width="thinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\tfrac {dy}{dx}}\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d638cbaa3b3e14dfbf4a9ff92e27760b84572e0" style="border: 0px; display: inline-block; height: 4.176ex; vertical-align: -1.338ex; width: 3.023ex;" /></span>menyatakan <a href="https://id.wikipedia.org/wiki/Turunan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan">turunan</a> dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> terhadap <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>. Rumus tersebut merangkum ide intuitif bahwa turunan dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> terhadap <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> adalah <a class="mw-disambig" href="https://id.wikipedia.org/wiki/Limit" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Limit">limit</a> dari rasio <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\tfrac {\Delta y}{\Delta x}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mrow><mi mathvariant="normal">Δ</mi><mi>�</mi></mrow><mrow><mi mathvariant="normal">Δ</mi><mi>�</mi></mrow></mfrac></mstyle></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\tfrac {\Delta y}{\Delta x}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3aa2e28168373c76134102582fee536a643bcf63" style="border: 0px; display: inline-block; height: 4.176ex; vertical-align: -1.338ex; width: 3.145ex;" /></span> saat <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \Delta x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi mathvariant="normal">Δ</mi><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \Delta x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3890eb866b6258d7a304fc34c70ee3fb3a81a70" style="border: 0px; display: inline-block; height: 2.176ex; vertical-align: -0.338ex; width: 3.266ex;" /></span> menuju 0.<p style="margin: 0.5em 0px 1em;"></p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Diferensial_sebagai_peta_linear">Diferensial sebagai peta linear</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Diferensial_(matematika)&veaction=edit&section=6&editintro=Template:Disambig_editintro" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Diferensial sebagai peta linear">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Diferensial_(matematika)&action=edit&section=6&editintro=Template:Disambig_editintro" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Diferensial sebagai peta linear">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;">Ada cara sederhana untuk mendefinisikan secara akurat makna diferensial, pertama menggunakan <a href="https://id.wikipedia.org/wiki/Garis_bilangan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Garis bilangan">garis bilangan</a> dengan mengganggapnya sebagai <a href="https://id.wikipedia.org/wiki/Peta_linear" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Peta linear">peta linear</a>. Hal ini selanjutnya dapat diperumum ke <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 1.678ex;" /></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} ^{n}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} ^{n}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" style="border: 0px; display: inline-block; height: 2.343ex; margin: 0px; vertical-align: -0.338ex; width: 2.897ex;" /></span>, <a href="https://id.wikipedia.org/wiki/Ruang_Hilbert" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Ruang Hilbert">ruang Hilbert</a>, <a href="https://id.wikipedia.org/wiki/Ruang_Banach" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Ruang Banach">ruang Banach</a>, atau secara umum, <a href="https://id.wikipedia.org/wiki/Ruang_vektor_topologis" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Ruang vektor topologis">ruang vektor topologis</a>. Kasus garis bilangan paling mudah untuk dijelaskan.</p><h4 style="color: black; font-size: 14px; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Diferensial_sebagai_peta_linear_pada_R">Diferensial sebagai peta linear pada R</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Diferensial_(matematika)&veaction=edit&section=7&editintro=Template:Disambig_editintro" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Diferensial sebagai peta linear pada R">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Diferensial_(matematika)&action=edit&section=7&editintro=Template:Disambig_editintro" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Diferensial sebagai peta linear pada R">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h4><p style="margin: 0.5em 0px 1em;">Misalkan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f(x)}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f(x)}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/202945cce41ecebb6f643f31d119c514bec7a074" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -0.838ex; width: 4.418ex;" /></span> adalah fungsi bernilai real pada <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 1.678ex;" /></span>. Variabel <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" style="border: 0px; display: inline-block; height: 1.676ex; margin: 0px; vertical-align: -0.338ex; width: 1.33ex;" /></span> dalam <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f(x)}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f(x)}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/202945cce41ecebb6f643f31d119c514bec7a074" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -0.838ex; width: 4.418ex;" /></span> dapat dianggap sebagai sebuah fungsi ketimbang sebuah bilangan, yakni sebagai <a href="https://id.wikipedia.org/wiki/Fungsi_identitas" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi identitas">fungsi identitas</a> pada <a href="https://id.wikipedia.org/wiki/Garis_bilangan_real" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Garis bilangan real">garis bilangan</a>, yang memetakan sebuah bilangan real <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle p}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle p}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" style="border: 0px; display: inline-block; height: 2.009ex; margin: 0px 0px 0px -0.089ex; vertical-align: -0.671ex; width: 1.259ex;" /></span> ke dirinya sendiri: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x(p)=p}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x(p)=p}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e4aabb9d6f7a9f7b24acabf008befa98385ca86" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -0.838ex; width: 8.576ex;" /></span>. Hal ini mengartikan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f(x)}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f(x)}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/202945cce41ecebb6f643f31d119c514bec7a074" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -0.838ex; width: 4.418ex;" /></span> adalah fungsi komposit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" style="border: 0px; display: inline-block; height: 2.509ex; margin: 0px; vertical-align: -0.671ex; width: 1.279ex;" /></span> terhadap <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" style="border: 0px; display: inline-block; height: 1.676ex; margin: 0px; vertical-align: -0.338ex; width: 1.33ex;" /></span>, dengan nilai di titik <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle p}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle p}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" style="border: 0px; display: inline-block; height: 2.009ex; margin: 0px 0px 0px -0.089ex; vertical-align: -0.671ex; width: 1.259ex;" /></span> adalah <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f(x(p))=f(p)}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>=</mo><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f(x(p))=f(p)}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d0bf9340067d5395bcaee48429f6251cf4c6841" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -0.838ex; width: 14.752ex;" /></span>. Diferensial <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \operatorname {d} f}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi mathvariant="normal">d</mi><mo></mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \operatorname {d} f}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96c037e09e925f5c3080de37c5475ef610453129" style="border: 0px; display: inline-block; height: 2.509ex; margin: 0px; vertical-align: -0.671ex; width: 2.958ex;" /></span> (yang tentunya bergantung pada perubahan nilai <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" style="border: 0px; display: inline-block; height: 2.509ex; margin: 0px; vertical-align: -0.671ex; width: 1.279ex;" /></span>) selanjutnya adalah sebuah <i>fungsi</i> di titik <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle p}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle p}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" style="border: 0px; display: inline-block; height: 2.009ex; margin: 0px 0px 0px -0.089ex; vertical-align: -0.671ex; width: 1.259ex;" /></span> (umumnya dinyatakan sebagai <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle df_{p}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub></mstyle></mrow></semantics></math></span><img alt="{\displaystyle df_{p}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1142d069553f6a55274e87055720127c02d3ec02" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -1.005ex; width: 3.414ex;" /></span>) yang memetakan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 1.678ex;" /></span> ke <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 1.678ex;" /></span> secara linear. Selanjutnya pemetaan linear dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 1.678ex;" /></span> ke <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 1.678ex;" /></span> dinyatakan oleh <a href="https://id.wikipedia.org/wiki/Matriks_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Matriks (matematika)">matriks</a> berukuran <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 1\times 1}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>1</mn><mo>×</mo><mn>1</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 1\times 1}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b4bf91a527dc01af9ef6ace81199becf1308e00" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 5.165ex;" /></span>, yang sama saja dengan sebuah bilangan, namun perubahan perspektif memungkinkan untuk mengganggap <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle df_{p}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub></mstyle></mrow></semantics></math></span><img alt="{\displaystyle df_{p}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1142d069553f6a55274e87055720127c02d3ec02" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -1.005ex; width: 3.414ex;" /></span> sebagai infinitesimal dan <i>membandingkannya</i> dengan <i>infinitesimal</i> <i>standar</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle dx_{p}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub></mstyle></mrow></semantics></math></span><img alt="{\displaystyle dx_{p}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29eb801f8265bc67ad79d20852df460a7b50b8c4" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -1.005ex; width: 3.605ex;" /></span>, yang dalam kasus ini adalah fungsi identitas dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 1.678ex;" /></span> ke <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 1.678ex;" /></span> (matriks berukuran <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 1\times 1}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>1</mn><mo>×</mo><mn>1</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 1\times 1}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b4bf91a527dc01af9ef6ace81199becf1308e00" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 5.165ex;" /></span> dengan elemen bernilai <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 1}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>1</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 1}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 1.162ex;" /></span>). Fungsi identitas memiliki sifat yakni jika <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \varepsilon }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \varepsilon }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a30c89172e5b88edbd45d3e2772c7f5e562e5173" style="border: 0px; display: inline-block; height: 1.676ex; margin: 0px; vertical-align: -0.338ex; width: 1.083ex;" /></span> bernilai sangat kecil, maka <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle dx_{p}(\varepsilon )}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle dx_{p}(\varepsilon )}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7725201829c09ebd77a3d6855a9229664fa4cd9" style="border: 0px; display: inline-block; height: 3.009ex; margin: 0px; vertical-align: -1.005ex; width: 6.498ex;" /></span> juga akan bernilai sangat kecil, memungkinkannya dianggap sebagai suatu infinitesimal. Diferensial <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle df_{p}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub></mstyle></mrow></semantics></math></span><img alt="{\displaystyle df_{p}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1142d069553f6a55274e87055720127c02d3ec02" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -1.005ex; width: 3.414ex;" /></span> memiliki sifat yang sama, karena ia merupakan kelipatan dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle dx_{p}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub></mstyle></mrow></semantics></math></span><img alt="{\displaystyle dx_{p}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29eb801f8265bc67ad79d20852df460a7b50b8c4" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -1.005ex; width: 3.605ex;" /></span>, dan besar kelipatan ini, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f'(p)}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mo>′</mo></msup><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f'(p)}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71159b6c94f0c2f8a4a88e0486a2bd0e95dafcbe" style="border: 0px; display: inline-block; height: 3.009ex; margin: 0px; vertical-align: -0.838ex; width: 4.984ex;" /></span>, adalah definisi dari turunan. Alhasil didapatkan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle df_{p}=f'(p)\,dx_{p}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo>=</mo><msup><mi>�</mi><mo>′</mo></msup><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub></mstyle></mrow></semantics></math></span><img alt="{\displaystyle df_{p}=f'(p)\,dx_{p}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02a29e57d4135aa64a8fd3df615d37b778cd6437" style="border: 0px; display: inline-block; height: 3.176ex; margin: 0px; vertical-align: -1.005ex; width: 15.489ex;" /></span>, dan akibatnya <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle df=f'\,dx}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mi>�</mi><mo>=</mo><msup><mi>�</mi><mo>′</mo></msup><mspace width="thinmathspace"></mspace><mi>�</mi><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle df=f'\,dx}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79c0c635464c5c6aee6ca78d32df5352f2745806" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -0.671ex; width: 10.531ex;" /></span>.</p><p style="margin: 0.5em 0px 1em;">Pendekatan di atas pada akhirnya menggunakan ide bahwa <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f'}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mo>′</mo></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f'}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/258eaada38956fb69b8cb1a2eef46bcb97d3126b" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -0.671ex; width: 2.005ex;" /></span> adalah perbandingan dari diferensial <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle df}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle df}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53181e2067a93b6bbf150042723cb059d9d2d26f" style="border: 0px; display: inline-block; height: 2.509ex; margin: 0px; vertical-align: -0.671ex; width: 2.494ex;" /></span> terhadap diferensial <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle dx}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle dx}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/845c817e348381a13f3fad5184169ce0e021c685" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 2.546ex;" /></span>. Pendekatan ini juga dapat diperumum karena berisi ide bahwa turunan dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" style="border: 0px; display: inline-block; height: 2.509ex; margin: 0px; vertical-align: -0.671ex; width: 1.279ex;" /></span> di titik <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle p}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle p}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" style="border: 0px; display: inline-block; height: 2.009ex; margin: 0px 0px 0px -0.089ex; vertical-align: -0.671ex; width: 1.259ex;" /></span> adalah <i>aproksimasi linear terbaik</i> dari fungsi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" style="border: 0px; display: inline-block; height: 2.509ex; margin: 0px; vertical-align: -0.671ex; width: 1.279ex;" /></span> di titik <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle p}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle p}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" style="border: 0px; display: inline-block; height: 2.009ex; margin: 0px 0px 0px -0.089ex; vertical-align: -0.671ex; width: 1.259ex;" /></span>.</p><h4 style="color: black; font-size: 14px; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Diferensial_sebagai_peta_linear_pada_Rn">Diferensial sebagai peta linear pada R<sup style="font-size: 11.2px; line-height: 1;">n</sup></span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Diferensial_(matematika)&veaction=edit&section=8&editintro=Template:Disambig_editintro" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Diferensial sebagai peta linear pada Rn">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Diferensial_(matematika)&action=edit&section=8&editintro=Template:Disambig_editintro" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Diferensial sebagai peta linear pada Rn">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h4><p style="margin: 0.5em 0px 1em;">Jika <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" style="border: 0px; display: inline-block; height: 2.509ex; margin: 0px; vertical-align: -0.671ex; width: 1.279ex;" /></span> adalah fungsi multivariabel dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} ^{n}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} ^{n}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" style="border: 0px; display: inline-block; height: 2.343ex; margin: 0px; vertical-align: -0.338ex; width: 2.897ex;" /></span> ke <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 1.678ex;" /></span>, maka <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" style="border: 0px; display: inline-block; height: 2.509ex; margin: 0px; vertical-align: -0.671ex; width: 1.279ex;" /></span> didefinisikan sebagai <i>terdiferensialkan</i><sup class="reference" id="cite_ref-7" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Diferensial_(matematika)#cite_note-7" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[7]</a></sup> di titik <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle p\in \mathbb {R} ^{n}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>∈</mo><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle p\in \mathbb {R} ^{n}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7d5b6202943d58e511d6616d84cd13ca0bc7547" style="border: 0px; display: inline-block; height: 2.676ex; margin: 0px 0px 0px -0.089ex; vertical-align: -0.671ex; width: 6.996ex;" /></span> jika terdapat pemetaan linear <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle df_{p}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub></mstyle></mrow></semantics></math></span><img alt="{\displaystyle df_{p}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1142d069553f6a55274e87055720127c02d3ec02" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -1.005ex; width: 3.414ex;" /></span> dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} ^{n}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} ^{n}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" style="border: 0px; display: inline-block; height: 2.343ex; margin: 0px; vertical-align: -0.338ex; width: 2.897ex;" /></span> ke <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 1.678ex;" /></span> sedemikian sehingga untuk sembarang <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \varepsilon >0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>></mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \varepsilon >0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e04ec3670b50384a3ce48aca42e7cc5131a06b12" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 5.344ex;" /></span>, ada suatu <a href="https://id.wikipedia.org/wiki/Lingkungan_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Lingkungan (matematika)">lingkungan</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle N}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle N}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 2.064ex;" /></span> dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle p}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle p}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" style="border: 0px; display: inline-block; height: 2.009ex; margin: 0px 0px 0px -0.089ex; vertical-align: -0.671ex; width: 1.259ex;" /></span> sedemikian sehigga untuk sembarang <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x\in N}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>∈</mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x\in N}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a76d49a16447f70b00dd86a78bd94916b0514e1" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 6.234ex;" /></span>,</p><div class="mwe-math-element" style="max-width: 100%; overflow-x: auto;"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; height: 1px; margin-bottom: 0.6em; margin-left: 1.6em !important; margin-right: auto; margin-top: 0.6em; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \left|f(x)-f(p)-df_{p}(x-p)\right|<\varepsilon \left|x-p\right|.}" display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow><mo>|</mo><mrow><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>−</mo><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>−</mo><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo stretchy="false">(</mo><mi>�</mi><mo>−</mo><mi>�</mi><mo stretchy="false">)</mo></mrow><mo>|</mo></mrow><mo><</mo><mi>�</mi><mrow><mo>|</mo><mrow><mi>�</mi><mo>−</mo><mi>�</mi></mrow><mo>|</mo></mrow><mo>.</mo></mstyle></mrow></semantics></math></div><img alt="{\displaystyle \left|f(x)-f(p)-df_{p}(x-p)\right|<\varepsilon \left|x-p\right|.}" aria-hidden="true" class="mwe-math-fallback-image-display mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5980fb479c9e411069149b67ee87574b9b3ea25d" style="border: 0px; display: block; height: 3.009ex; margin-bottom: 0.6em; margin-left: 1.6em !important; margin-right: auto !important; margin-top: 0.6em; vertical-align: -1.005ex; width: 38.449ex;" /></div>Pendekatan yang sama dengan kasus satu dimensi dapat digunakan pada masalah ini, dengan menganggap ekspresi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f(x_{1},x_{2},\ldots ,x_{n})}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo stretchy="false">)</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f(x_{1},x_{2},\ldots ,x_{n})}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f25b8df72ba6491812f45e36e4938ad3385def1" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.838ex; width: 16.616ex;" /></span> sebagai fungsi komposit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 1.279ex;" /></span> dengan fungsi koordinat standar <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1},x_{2},\ldots ,x_{n}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1},x_{2},\ldots ,x_{n}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8694289524164f895d6665f163e14c4dc5ec648d" style="border: 0px; display: inline-block; height: 2.009ex; vertical-align: -0.671ex; width: 13.528ex;" /></span> on <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} ^{n}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} ^{n}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" style="border: 0px; display: inline-block; height: 2.343ex; vertical-align: -0.338ex; width: 2.897ex;" /></span> (yakni <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{j}(p)}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{j}(p)}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffbc4509c3230bedf96b00363956aa7515d15597" style="border: 0px; display: inline-block; height: 3.009ex; vertical-align: -1.005ex; width: 5.218ex;" /></span> menyatakan komponen ke-<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle j}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle j}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" style="border: 0px; display: inline-block; height: 2.509ex; margin-left: -0.027ex; vertical-align: -0.671ex; width: 0.985ex;" /></span> dari titik <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle p\in \mathbb {R} ^{n}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>∈</mo><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle p\in \mathbb {R} ^{n}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7d5b6202943d58e511d6616d84cd13ca0bc7547" style="border: 0px; display: inline-block; height: 2.676ex; margin-left: -0.089ex; vertical-align: -0.671ex; width: 6.996ex;" /></span>). Selanjutnya diferensial<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \left(dx_{1}\right)_{p},\left(dx_{2}\right)_{p},\ldots ,\left(dx_{n}\right)_{p}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mrow><mo>(</mo><mrow><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo>,</mo><msub><mrow><mo>(</mo><mrow><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mo>(</mo><mrow><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \left(dx_{1}\right)_{p},\left(dx_{2}\right)_{p},\ldots ,\left(dx_{n}\right)_{p}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1915bc551395809621a0904b4acda7aaab1efb3a" style="border: 0px; display: inline-block; height: 3.176ex; vertical-align: -1.171ex; width: 25.781ex;" /></span> pada titik <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle p}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle p}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" style="border: 0px; display: inline-block; height: 2.009ex; margin-left: -0.089ex; vertical-align: -0.671ex; width: 1.259ex;" /></span> membentuk sebuah <a href="https://id.wikipedia.org/wiki/Basis_(aljabar_linear)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Basis (aljabar linear)">basis</a> untuk <a href="https://id.wikipedia.org/wiki/Ruang_vektor" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Ruang vektor">ruang vektor</a> dari peta-peta linear <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} ^{n}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} ^{n}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" style="border: 0px; display: inline-block; height: 2.343ex; vertical-align: -0.338ex; width: 2.897ex;" /></span> ke <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" style="border: 0px; display: inline-block; height: 2.176ex; vertical-align: -0.338ex; width: 1.678ex;" /></span>. Akibatnya, jika <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 1.279ex;" /></span> terdiferensialkan pada titik <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle p}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle p}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" style="border: 0px; display: inline-block; height: 2.009ex; margin-left: -0.089ex; vertical-align: -0.671ex; width: 1.259ex;" /></span>, maka <i><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \operatorname {d} f_{p}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi mathvariant="normal">d</mi><mo></mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \operatorname {d} f_{p}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d57e5bfe93b171364c27e2a17df61d97eae34c69" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -1.005ex; width: 3.878ex;" /></i> dapat ditulis sebagai <a href="https://id.wikipedia.org/wiki/Kombinasi_linear" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kombinasi linear">kombinasi linear</a> elemen-elemen basis tersebut:<div class="mwe-math-element" style="max-width: 100%; overflow-x: auto;"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; height: 1px; margin-bottom: 0.6em; margin-left: 1.6em !important; margin-right: auto; margin-top: 0.6em; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle df_{p}=\sum _{j=1}^{n}D_{j}f(p)\,(dx_{j})_{p}.}" display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo>=</mo><munderover><mo>∑</mo><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mo>=</mo><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></munderover><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace><mo stretchy="false">(</mo><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><msub><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo>.</mo></mstyle></mrow></semantics></math></div><img alt="{\displaystyle df_{p}=\sum _{j=1}^{n}D_{j}f(p)\,(dx_{j})_{p}.}" aria-hidden="true" class="mwe-math-fallback-image-display mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b86b7d9325b42462abb1dfef5683590981c929b" style="border: 0px; display: block; height: 7.176ex; margin-bottom: 0.6em; margin-left: 1.6em !important; margin-right: auto !important; margin-top: 0.6em; vertical-align: -3.338ex; width: 24.704ex;" /></div>Koefisien-koefisien <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle D_{j}f(p)}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle D_{j}f(p)}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b0c00373ed02572aa7ebfaa00287e865c9ab290" style="border: 0px; display: inline-block; height: 3.009ex; vertical-align: -1.005ex; width: 7.091ex;" /></span> adalah (dari definisi) <a href="https://id.wikipedia.org/wiki/Turunan_parsial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan parsial">turunan parsial</a> dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 1.279ex;" /></span> di <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle p}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle p}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" style="border: 0px; display: inline-block; height: 2.009ex; margin-left: -0.089ex; vertical-align: -0.671ex; width: 1.259ex;" /></span> terhadap <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1},x_{2},\ldots ,x_{n}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1},x_{2},\ldots ,x_{n}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8694289524164f895d6665f163e14c4dc5ec648d" style="border: 0px; display: inline-block; height: 2.009ex; vertical-align: -0.671ex; width: 13.528ex;" /></span>. Dengan kata lain, jika <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 1.279ex;" /></span> terdiferensialkan di keseluruhan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} ^{n}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} ^{n}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" style="border: 0px; display: inline-block; height: 2.343ex; vertical-align: -0.338ex; width: 2.897ex;" /></span>, maka diferensial <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle df}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle df}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53181e2067a93b6bbf150042723cb059d9d2d26f" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 2.494ex;" /></span> dapat ditulis dengan lebih ringkas sebagai:<div class="mwe-math-element" style="max-width: 100%; overflow-x: auto;"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; height: 1px; margin-bottom: 0.6em; margin-left: 1.6em !important; margin-right: auto; margin-top: 0.6em; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle df={\frac {\partial f}{\partial x_{1}}}\,dx_{1}+{\frac {\partial f}{\partial x_{2}}}\,dx_{2}+\cdots +{\frac {\partial f}{\partial x_{n}}}\,dx_{n}.}" display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mi>�</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi mathvariant="normal">∂</mi><mi>�</mi></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub></mrow></mfrac></mrow><mspace width="thinmathspace"></mspace><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi mathvariant="normal">∂</mi><mi>�</mi></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub></mrow></mfrac></mrow><mspace width="thinmathspace"></mspace><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>+</mo><mo>⋯</mo><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi mathvariant="normal">∂</mi><mi>�</mi></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub></mrow></mfrac></mrow><mspace width="thinmathspace"></mspace><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo>.</mo></mstyle></mrow></semantics></math></div><img alt="{\displaystyle df={\frac {\partial f}{\partial x_{1}}}\,dx_{1}+{\frac {\partial f}{\partial x_{2}}}\,dx_{2}+\cdots +{\frac {\partial f}{\partial x_{n}}}\,dx_{n}.}" aria-hidden="true" class="mwe-math-fallback-image-display mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9422ff76e3193e234eff6f3e3911c9cefa3796e7" style="border: 0px; display: block; height: 6.009ex; margin-bottom: 0.6em; margin-left: 1.6em !important; margin-right: auto !important; margin-top: 0.6em; vertical-align: -2.338ex; width: 43.388ex;" /></div>Pada kasus satu dimensi persamaan di atas menjadi<div class="mwe-math-element" style="max-width: 100%; overflow-x: auto;"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; height: 1px; margin-bottom: 0.6em; margin-left: 1.6em !important; margin-right: auto; margin-top: 0.6em; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle df={\frac {df}{dx}}dx}" display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mi>�</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi>�</mi><mi>�</mi></mrow><mrow><mi>�</mi><mi>�</mi></mrow></mfrac></mrow><mi>�</mi><mi>�</mi></mstyle></mrow></semantics></math></div><img alt="{\displaystyle df={\frac {df}{dx}}dx}" aria-hidden="true" class="mwe-math-fallback-image-display mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65c642a7b555ece7647a9227b5da4e5714a544b3" style="border: 0px; display: block; height: 5.509ex; margin-bottom: 0.6em; margin-left: 1.6em !important; margin-right: auto !important; margin-top: 0.6em; vertical-align: -2.005ex; width: 11.52ex;" /></div>sama seperti hasil pada kasus satu dimensi. Ide ini dapat diperumum untuk fungsi dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} ^{n}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} ^{n}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" style="border: 0px; display: inline-block; height: 2.343ex; vertical-align: -0.338ex; width: 2.897ex;" /></span> ke <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} ^{m}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} ^{m}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a87a024931038d1858dc22e8a194e5978c3412e" style="border: 0px; display: inline-block; height: 2.343ex; vertical-align: -0.338ex; width: 3.353ex;" /></span>. Lebih lanjut, definisi ini lebih menguntungkan ketimbang definisi-definisi turunan yang lain karena bersifat <a class="new" href="https://id.wikipedia.org/w/index.php?title=Invarian_(matematika)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Invarian (matematika) (halaman belum tersedia)">invarian</a> terhadap perubahan koordinat. Hal ini mengartikan ide yang sama juga dapat digunakan untuk mendefinisikan diferensial dari <a class="new" href="https://id.wikipedia.org/w/index.php?title=Pemetaan_mulus&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Pemetaan mulus (halaman belum tersedia)">pemetaan mulus</a> dari <a href="https://id.wikipedia.org/wiki/Lipatan_terdiferensialkan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Lipatan terdiferensialkan">lipatan mulus</a>.<p style="margin: 0.5em 0px 1em;"></p><p style="margin: 0.5em 0px 1em;">Walaupun demikian, perlu disadari bahwa keberadaan semua <a href="https://id.wikipedia.org/wiki/Turunan_parsial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan parsial">turunan parsial</a> dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f(x)}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f(x)}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/202945cce41ecebb6f643f31d119c514bec7a074" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -0.838ex; width: 4.418ex;" /></span> di <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" style="border: 0px; display: inline-block; height: 1.676ex; margin: 0px; vertical-align: -0.338ex; width: 1.33ex;" /></span> adalah <a class="new" href="https://id.wikipedia.org/w/index.php?title=Syarat_perlu_dan_syarat_cukup&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Syarat perlu dan syarat cukup (halaman belum tersedia)">syarat perlu</a> untuk keberadaan suatu diferensial di titik <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" style="border: 0px; display: inline-block; height: 1.676ex; margin: 0px; vertical-align: -0.338ex; width: 1.33ex;" /></span>. Namun itu bukan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Syarat_cukup&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Syarat cukup (halaman belum tersedia)">syarat cukup</a>, untuk contoh penangkal, lihat <a class="new" href="https://id.wikipedia.org/w/index.php?title=Turunan_Gateaux&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan Gateaux (halaman belum tersedia)">turunan Gateaux</a>.</p></div></div></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8185710560472973854.post-44625085640418589692024-01-29T13:46:00.005+07:002024-01-29T13:46:56.168+07:00Persamaan Kuadrat<p> </p><header class="mw-body-header vector-page-titlebar" style="align-items: center; background-color: white; box-shadow: none; color: #202122; display: flex; flex-wrap: nowrap; font-family: sans-serif; font-size: 16px; grid-area: titlebar / titlebar / titlebar / titlebar; justify-content: flex-end; position: relative;"><h1 class="firstHeading mw-first-heading" id="firstHeading" style="border: 0px; color: black; flex-grow: 1; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-size: 1.8em; font-weight: normal; line-height: 1.375; margin: 0px; overflow-wrap: break-word; overflow: hidden; padding: 0px;"><span class="mw-page-title-main">Persamaan kuadrat</span></h1><div class="vector-dropdown mw-portlet mw-portlet-lang" id="p-lang-btn" style="box-sizing: border-box; flex-shrink: 0; float: right; margin-right: -12px; position: relative;"><input aria-haspopup="true" aria-label="Pergi ke artikel dalam bahasa lain. 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border-top: 1px solid transparent; color: #202122; font-family: sans-serif; font-size: 16px; grid-area: columnEnd / columnEnd / columnEnd / columnEnd; margin-top: 1.8em; overflow-anchor: none;"><div class="vector-sticky-pinned-container" style="box-sizing: border-box; contain: paint; max-height: calc(100vh - 48px); overflow: hidden auto; position: sticky; top: 24px;"></div></div><div aria-labelledby="firstHeading" class="vector-body ve-init-mw-desktopArticleTarget-targetContainer" data-mw-ve-target-container="" id="bodyContent" style="background-color: white; color: #202122; font-family: sans-serif; font-size: var(--font-size-medium); grid-area: content / content / content / content; line-height: var(--line-height-medium); position: relative; z-index: 0;"><div class="vector-body-before-content" style="overflow: hidden;"><div class="mw-indicators" style="float: right; font-size: 0.875em; line-height: 1.6; margin-top: 8px; padding-top: 0.4em; position: relative; z-index: 1;"></div><div class="noprint" id="siteSub" style="font-size: 11.2px; margin-top: 8px;">Dari Wikipedia bahasa Indonesia, ensiklopedia bebas</div></div><div id="contentSub" style="color: #54595d; font-size: 0.875rem; margin: 8px 0px 0px; width: auto;"><div id="mw-content-subtitle"></div></div><div class="mw-body-content" id="mw-content-text" style="margin-top: 16px;"><div class="mw-content-ltr mw-parser-output" dir="ltr" lang="id"><div class="hatnote navigation-not-searchable" role="note" style="font-style: italic; margin-bottom: 0.5em; padding-left: 1.6em;">Halaman ini berisi artikel tentang persamaan aljabar derajat dua dan solusi. Untuk rumus yang digunakan untuk mencari solusi persamaan tersebut, lihat <a href="https://id.wikipedia.org/wiki/Rumus_kuadrat" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Rumus kuadrat">Rumus kuadrat</a>. Untuk fungsi yang ditentukan oleh polinomial derajat dua, lihat <a href="https://id.wikipedia.org/wiki/Fungsi_kuadrat" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi kuadrat">Fungsi kuadrat</a>.</div><div class="side-box metadata side-box-right" style="background-color: #f9f9f9; border: 1px solid rgb(170, 170, 170); box-sizing: border-box; clear: right; float: right; font-size: 12.32px; line-height: 1.25em; margin: 4px 0px 4px 1em; width: 238px;"><div class="side-box-flex" style="align-items: center; display: flex;"><div class="side-box-text plainlist" style="flex: 1 1 0%; padding: 0.25em 0.9em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 14.5376px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mo>−</mo><mi>�</mi><mo>±</mo><mrow class="MJX-TeXAtom-ORD"><msqrt><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−</mo><mn>4</mn><mi>�</mi><mi>�</mi></msqrt></mrow></mrow><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00c22777378f9c594c71158fea8946f2495f2a28" style="border: 0px; display: inline-block; height: 6.176ex; vertical-align: -1.838ex; width: 21.525ex;" /></span></div></div><div class="side-box-abovebelow" style="padding: 0.25em 0.9em;"><a href="https://id.wikipedia.org/wiki/Rumus_kuadrat" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Rumus kuadrat">Rumus kuadrat</a> untuk akar dari persamaan kuadrat umum</div></div><p style="margin: 0.5em 0px 1em;"><b>Persamaan kuadrat</b> adalah suatu persamaanberorde dua. Bentuk umum dari <a href="https://id.wikipedia.org/wiki/Persamaan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Persamaan">persamaan</a> <a class="mw-disambig" href="https://id.wikipedia.org/wiki/Kuadrat" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kuadrat">kuadrat</a> adalah</p><p style="margin: 0.5em 0px 1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y=ax^{2}+bx+c\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><mi>�</mi><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>�</mi><mi>�</mi><mo>+</mo><mi>�</mi><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y=ax^{2}+bx+c\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0b9475a045bef701b10fb8baea9dd91191a1659" style="border: 0px; display: inline-block; height: 3.009ex; margin: 0px -0.387ex 0px 0px; vertical-align: -0.671ex; width: 17.27ex;" /></span></p><p style="margin: 0.5em 0px 1em;">dengan cara</p><p style="margin: 0.5em 0px 1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle a\neq 0\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>≠</mo><mn>0</mn><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle a\neq 0\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/808dd60c09d686420928d3cc5395f8b72130b1a6" style="border: 0px; display: inline-block; height: 2.676ex; margin: 0px -0.387ex 0px 0px; vertical-align: -0.838ex; width: 5.878ex;" /></span></p><p style="margin: 0.5em 0px 1em;">Huruf-huruf <i>a</i>, <i>b</i> dan <i>c</i> disebut sebagai koefisien: koefisien kuadrat <i>a</i> adalah koefisien dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x^{2}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x^{2}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf0bf28fd28f45d07e1ceb909ce333c18c558c93" style="border: 0px; display: inline-block; height: 2.676ex; margin: 0px; vertical-align: -0.338ex; width: 2.384ex;" /></span>, koefisien linier <i>b</i> adalah koefisien dari <i>x</i>, dan <i>c</i> adalah koefisien konstan atau disebut juga suku bebas.</p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span id="Arti_nilai_a.2C_b.2C_dan_c"></span><span class="mw-headline" id="Arti_nilai_a,_b,_dan_c">Arti nilai a, b, dan c</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&veaction=edit&section=1" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Arti nilai a, b, dan c">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&action=edit&section=1" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Arti nilai a, b, dan c">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><table style="font-size: 14px;"><tbody><tr><td><figure style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Kuadrat-a.png" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img class="mw-file-element" data-file-height="400" data-file-width="400" decoding="async" height="200" src="https://upload.wikimedia.org/wikipedia/id/thumb/a/a3/Kuadrat-a.png/200px-Kuadrat-a.png" srcset="//upload.wikimedia.org/wikipedia/id/thumb/a/a3/Kuadrat-a.png/300px-Kuadrat-a.png 1.5x, //upload.wikimedia.org/wikipedia/id/a/a3/Kuadrat-a.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="200" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Variasi nilai a</figcaption></figure></td><td><figure style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Kuadrat-b.png" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img class="mw-file-element" data-file-height="400" data-file-width="400" decoding="async" height="200" src="https://upload.wikimedia.org/wikipedia/id/thumb/f/f1/Kuadrat-b.png/200px-Kuadrat-b.png" srcset="//upload.wikimedia.org/wikipedia/id/thumb/f/f1/Kuadrat-b.png/300px-Kuadrat-b.png 1.5x, //upload.wikimedia.org/wikipedia/id/f/f1/Kuadrat-b.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="200" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Variasi nilai b</figcaption></figure></td><td><figure style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Kuadrat-c.png" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img class="mw-file-element" data-file-height="400" data-file-width="400" decoding="async" height="200" src="https://upload.wikimedia.org/wikipedia/id/thumb/4/48/Kuadrat-c.png/200px-Kuadrat-c.png" srcset="//upload.wikimedia.org/wikipedia/id/thumb/4/48/Kuadrat-c.png/300px-Kuadrat-c.png 1.5x, //upload.wikimedia.org/wikipedia/id/4/48/Kuadrat-c.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="200" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Variasi nilai c</figcaption></figure></td></tr></tbody></table><p style="margin: 0.5em 0px 1em;">Nilai-nilai <i>a</i>, <i>b</i> dan <i>c</i> menentukan bagaimana bentuk parabola dari fungsi persamaan kuadrat dalam ruang <i>xy</i>.</p><ul style="list-style-image: url("/w/skins/Vector/resources/skins.vector.styles/images/bullet-icon.svg?d4515"); margin: 0.3em 0px 0px 1.6em; padding: 0px;"><li style="margin-bottom: 0.1em;"><i>a</i> menentukan seberapa cekung/cembung parabola yang dibentuk oleh fungsi kuadrat. Nilai <i>a > 0</i> akan menyebabkan parabola terbuka ke atas, sedangkan nilai <i>a < 0</i> akan menyebabkan parabola terbuka ke bawah.</li><li style="margin-bottom: 0.1em;"><i>b</i> menentukan kira-kira posisi <i>x</i> puncak parabola, atau sumbu simetri cermin dari kurva yang dibentuk. Posisi tepatnya adalah <i>-b/2a</i>.</li><li style="margin-bottom: 0.1em;"><i>c</i> menentukan titik potong fungsi parabola yang dibentuk dengan sumbu <i>y</i> atau saat <i>x = 0</i>.</li></ul><p style="margin: 0.5em 0px 1em;">Ilustrasi grafik-grafik persamaan kuadrat dengan berbagai variasi nilai <i>a</i>. <i>b</i> dan <i>c</i> dapat dilihat pada gambar diatas.</p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span id="Rumus_Kuadratis_.28Rumus_abc.29"></span><span class="mw-headline" id="Rumus_Kuadratis_(Rumus_abc)">Rumus Kuadratis (Rumus abc)</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&veaction=edit&section=2" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Rumus Kuadratis (Rumus abc)">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&action=edit&section=2" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Rumus Kuadratis (Rumus abc)">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><figure style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Kuadrat-akar.png" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img class="mw-file-element" data-file-height="400" data-file-width="400" decoding="async" height="300" src="https://upload.wikimedia.org/wikipedia/id/thumb/d/d5/Kuadrat-akar.png/300px-Kuadrat-akar.png" srcset="//upload.wikimedia.org/wikipedia/id/d/d5/Kuadrat-akar.png 1.5x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="300" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">y = 0.75 (x + 3.333) (x - 6-000)</figcaption></figure><p style="margin: 0.5em 0px 1em;">Rumus kuadratis dikenal pula dengan nama <b>rumus abc</b> karena digunakan untuk menghitung akar-akar persamaan kuadrat yang tergantung dari nilai-nilai <i>a</i>, <i>b</i> dan <i>c</i> suatu persamaan kuadrat. Rumus yang dimaksud memiliki bentuk</p><p style="margin: 0.5em 0px 1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1,2}={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mo>−</mo><mi>�</mi><mo>±</mo><mrow class="MJX-TeXAtom-ORD"><msqrt><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−</mo><mn>4</mn><mi>�</mi><mi>�</mi></msqrt></mrow></mrow><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1,2}={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a62e1c4fb012beb24706443a8482872d6c36b667" style="border: 0px; display: inline-block; height: 6.176ex; margin: 0px; vertical-align: -1.838ex; width: 23.859ex;" /></span></p><p style="margin: 0.5em 0px 1em;">Rumus ini digunakan untuk mencari akar-akar persamaan kuadrat apabila dinyatakan bahwa</p><p style="margin: 0.5em 0px 1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y=0\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><mn>0</mn><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y=0\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ea7c378f8da6bf071e6bd94fefb8ca200ad3fc2" style="border: 0px; display: inline-block; height: 2.509ex; margin: 0px -0.387ex 0px 0px; vertical-align: -0.671ex; width: 5.804ex;" /></span>.</p><p style="margin: 0.5em 0px 1em;">Dari rumus tersebut akan diperoleh akar-akar persamaan, sehingga persamaan semula dalam bentuk</p><p style="margin: 0.5em 0px 1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y=ax^{2}+bx+c\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><mi>�</mi><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>�</mi><mi>�</mi><mo>+</mo><mi>�</mi><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y=ax^{2}+bx+c\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0b9475a045bef701b10fb8baea9dd91191a1659" style="border: 0px; display: inline-block; height: 3.009ex; margin: 0px -0.387ex 0px 0px; vertical-align: -0.671ex; width: 17.27ex;" /></span></p><p style="margin: 0.5em 0px 1em;">dapat dituliskan menjadi</p><p style="margin: 0.5em 0px 1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y=a(x-x_{1})(x-x_{2})\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo>−</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>�</mi><mo>−</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y=a(x-x_{1})(x-x_{2})\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d87163721c183e0474da2fb2ab3b34e70f6fbfe" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px -0.387ex 0px 0px; vertical-align: -0.838ex; width: 22.597ex;" /></span>.</p><p style="margin: 0.5em 0px 1em;">Dari persamaan terakhir ini dapat pula dituliskan dua hubungan yang telah umum dikenal, yaitu</p><p style="margin: 0.5em 0px 1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}+x_{2}=-{\frac {b}{a}}\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>=</mo><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}+x_{2}=-{\frac {b}{a}}\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f386ed8866e42dedde263ee3a3a69ed85e83a2b5" style="border: 0px; display: inline-block; height: 5.343ex; margin: 0px -0.387ex 0px 0px; vertical-align: -1.838ex; width: 14.968ex;" /></span></p><p style="margin: 0.5em 0px 1em;">dan</p><p style="margin: 0.5em 0px 1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}\cdot x_{2}={\frac {c}{a}}\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>⋅</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}\cdot x_{2}={\frac {c}{a}}\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29f455b426e8e569404d450268a40325f46844c1" style="border: 0px; display: inline-block; height: 4.676ex; margin: 0px -0.387ex 0px 0px; vertical-align: -1.838ex; width: 11.998ex;" /></span>.</p><p style="margin: 0.5em 0px 1em;">Ilustrasi dapat dilihat pada gambar.</p><p style="margin: 0.5em 0px 1em;"><br /></p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dt style="font-weight: bold; margin-bottom: 0.1em;">Sifat akar persamaan kuadrat</dt></dl><table class="wikitable" style="background-color: #f8f9fa; border-collapse: collapse; border: 1px solid rgb(162, 169, 177); color: #202122; font-size: 14px; margin: 1em 0px;"><caption style="font-weight: bold;"></caption><tbody><tr><th style="background-color: #eaecf0; border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em; text-align: center;">Hubungan</th><th style="background-color: #eaecf0; border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em; text-align: center;">Syarat</th></tr><tr><td rowspan="3" style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;">Kedua akar real tandanya positif</td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle D\geq 0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>≥</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle D\geq 0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa2cc455106dd53a8f81561e4077e415c0e032dc" style="border: 0px; display: inline-block; height: 2.343ex; vertical-align: -0.505ex; width: 6.185ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}+x_{2}>0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>></mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}+x_{2}>0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd79ae53f90e3e3223c26b22876b55f958a82420" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 11.869ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}\cdot x_{2}>0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>⋅</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>></mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}\cdot x_{2}>0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a54121204df5e22281f9d496d967c1baffde0b3" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 10.708ex;" /></span></td></tr><tr><td rowspan="3" style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;">Kedua akar real tandanya negatif</td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle D\geq 0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>≥</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle D\geq 0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa2cc455106dd53a8f81561e4077e415c0e032dc" style="border: 0px; display: inline-block; height: 2.343ex; vertical-align: -0.505ex; width: 6.185ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}+x_{2}<0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo><</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}+x_{2}<0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74fa3c430760c89abdeb8f7a0b56203d0d81b1be" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 11.869ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}\cdot x_{2}>0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>⋅</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>></mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}\cdot x_{2}>0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a54121204df5e22281f9d496d967c1baffde0b3" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 10.708ex;" /></span></td></tr><tr><td rowspan="2" style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;">Kedua akar real tandanya berlainan</td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle D\geq 0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>≥</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle D\geq 0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa2cc455106dd53a8f81561e4077e415c0e032dc" style="border: 0px; display: inline-block; height: 2.343ex; vertical-align: -0.505ex; width: 6.185ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}\cdot x_{2}<0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>⋅</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo><</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}\cdot x_{2}<0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b71b669a1a6d946fa6211352cfd8109966def99c" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 10.708ex;" /></span></td></tr><tr><td rowspan="2" style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;">Kedua akar real sama</td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle D\geq 0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>≥</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle D\geq 0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa2cc455106dd53a8f81561e4077e415c0e032dc" style="border: 0px; display: inline-block; height: 2.343ex; vertical-align: -0.505ex; width: 6.185ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}\cdot x_{2}>0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>⋅</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>></mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}\cdot x_{2}>0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a54121204df5e22281f9d496d967c1baffde0b3" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 10.708ex;" /></span></td></tr><tr><td rowspan="2" style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;">Kedua akar real berkebalikan</td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle D>0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>></mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle D>0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/364065378f034883c14d3a3000ebccc021bd2105" style="border: 0px; display: inline-block; height: 2.176ex; vertical-align: -0.338ex; width: 6.185ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}+x_{2}=0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}+x_{2}=0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9819257c0ec8ff3c99ffc6e755d29fd0a49cd8b" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 11.869ex;" /></span></td></tr><tr><td rowspan="2" style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;">Kedua akar real berlawanan</td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle D>0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>></mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle D>0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/364065378f034883c14d3a3000ebccc021bd2105" style="border: 0px; display: inline-block; height: 2.176ex; vertical-align: -0.338ex; width: 6.185ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}\cdot x_{2}=1}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>⋅</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>=</mo><mn>1</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}\cdot x_{2}=1}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7dfbe5169d4081e8304d5df6dc0165efcec05a9b" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 10.708ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;">Akar tidak real (imajiner)</td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle D<0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo><</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle D<0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/533c6100feca217e3212231f4a5ab7342bacdbf0" style="border: 0px; display: inline-block; height: 2.176ex; vertical-align: -0.338ex; width: 6.185ex;" /></span></td></tr></tbody></table><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Persamaan_kuadrat_baru">Persamaan kuadrat baru</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&veaction=edit&section=3" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Persamaan kuadrat baru">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&action=edit&section=3" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Persamaan kuadrat baru">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><p style="margin: 0.5em 0px 1em;">Pokok umum persamaan kuadrat baru yaitu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x^{2}-(x_{1}+x_{2})x+x_{1}\cdot x_{2}=0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−</mo><mo stretchy="false">(</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo><mi>�</mi><mo>+</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>⋅</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x^{2}-(x_{1}+x_{2})x+x_{1}\cdot x_{2}=0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/242d57ddb9934a1d309ef2f636e53a3c0473693d" style="border: 0px; display: inline-block; height: 3.176ex; margin: 0px; vertical-align: -0.838ex; width: 29.52ex;" /></span></p><table class="wikitable" style="background-color: #f8f9fa; border-collapse: collapse; border: 1px solid rgb(162, 169, 177); color: #202122; font-size: 14px; margin: 1em 0px;"><caption style="font-weight: bold;"></caption><tbody><tr><th style="background-color: #eaecf0; border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em; text-align: center;">Persamaan kuadrat lama</th><th style="background-color: #eaecf0; border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em; text-align: center;">Persamaan kuadrat baru</th></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}+n{dan}x_{2}+n}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>+</mo><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mi>�</mi><mi>�</mi></mrow><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>+</mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}+n{dan}x_{2}+n}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/adec9cff22ad1c7d49af0ab164c6e8b3cc31ed48" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 17.078ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle a(x-n)^{2}+b(x-n)+c=0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo>−</mo><mi>�</mi><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo>−</mo><mi>�</mi><mo stretchy="false">)</mo><mo>+</mo><mi>�</mi><mo>=</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle a(x-n)^{2}+b(x-n)+c=0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0720ad6331d9e710e6997fe8c01d366ea752afd6" style="border: 0px; display: inline-block; height: 3.176ex; vertical-align: -0.838ex; width: 28.978ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}-n{dan}x_{2}-n}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>−</mo><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mi>�</mi><mi>�</mi></mrow><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>−</mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}-n{dan}x_{2}-n}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/033295a68c07b1884c3394e30dba431503415b65" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 17.078ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle a(x+n)^{2}+b(x+n)+c=0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo>+</mo><mi>�</mi><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo>+</mo><mi>�</mi><mo stretchy="false">)</mo><mo>+</mo><mi>�</mi><mo>=</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle a(x+n)^{2}+b(x+n)+c=0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/825173c408dccdac54098668221750069e126c6f" style="border: 0px; display: inline-block; height: 3.176ex; vertical-align: -0.838ex; width: 28.978ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle n\cdot x_{1}{dan}n\cdot x_{2}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>⋅</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mi>�</mi><mi>�</mi></mrow><mi>�</mi><mo>⋅</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub></mstyle></mrow></semantics></math></span><img alt="{\displaystyle n\cdot x_{1}{dan}n\cdot x_{2}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5d56223958259e1077c6561c7df39053175afcb" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 14.756ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle a({\frac {x}{n}})^{2}+b({\frac {x}{n}})+c=0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>�</mi><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mo stretchy="false">)</mo><mo>+</mo><mi>�</mi><mo>=</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle a({\frac {x}{n}})^{2}+b({\frac {x}{n}})+c=0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/286c36e65f2640c730d51c0f1d5e54b48b31b657" style="border: 0px; display: inline-block; height: 4.676ex; vertical-align: -1.838ex; width: 22.31ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\frac {x_{1}}{n}}{dan}{\frac {x_{2}}{n}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mfrac><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mi>�</mi></mfrac></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mi>�</mi><mi>�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mfrac><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mi>�</mi></mfrac></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\frac {x_{1}}{n}}{dan}{\frac {x_{2}}{n}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc8c74edbb78089f0272ada310a98d3cae37c292" style="border: 0px; display: inline-block; height: 4.676ex; vertical-align: -1.838ex; width: 10.281ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle a(nx)^{2}+b(nx)+c=0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mi>�</mi><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mi>�</mi><mo stretchy="false">)</mo><mo>+</mo><mi>�</mi><mo>=</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle a(nx)^{2}+b(nx)+c=0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b21cc8f49f4d7a2aaa8dd4266de5634a1863610d" style="border: 0px; display: inline-block; height: 3.176ex; vertical-align: -0.838ex; width: 23.298ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {x_{1}}^{2}{dan}{x_{2}}^{2}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow class="MJX-TeXAtom-ORD"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub></mrow><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mi>�</mi><mi>�</mi></mrow><msup><mrow class="MJX-TeXAtom-ORD"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub></mrow><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {x_{1}}^{2}{dan}{x_{2}}^{2}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5a4379ca742acb04339f221a6f3769a98ff0027a" style="border: 0px; display: inline-block; height: 3.009ex; vertical-align: -0.671ex; width: 10.717ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle a^{2}x^{2}+(2ac-b^{2})x+c^{2}=0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mo stretchy="false">(</mo><mn>2</mn><mi>�</mi><mi>�</mi><mo>−</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo stretchy="false">)</mo><mi>�</mi><mo>+</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>=</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle a^{2}x^{2}+(2ac-b^{2})x+c^{2}=0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e493a5bc8d657e9f69839dacbe7beeefd3aa7145" style="border: 0px; display: inline-block; height: 3.176ex; vertical-align: -0.838ex; width: 28.101ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\sqrt {x_{1}}}{dan}{\sqrt {x_{2}}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><msqrt><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub></msqrt></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mi>�</mi><mi>�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><msqrt><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub></msqrt></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\sqrt {x_{1}}}{dan}{\sqrt {x_{2}}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb1764681178d12f174244b2d8f595de73623164" style="border: 0px; display: inline-block; height: 3.009ex; vertical-align: -1.171ex; width: 12.48ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ax^{4}+bx^{2}+c=0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>4</mn></mrow></msup><mo>+</mo><mi>�</mi><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>�</mi><mo>=</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ax^{4}+bx^{2}+c=0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76da3e4d0b41df07961b4c31d29d2bdaf1c76a3d" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.505ex; width: 17.944ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\frac {1}{x_{1}}}{dan}{\frac {1}{x_{2}}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub></mfrac></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mi>�</mi><mi>�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub></mfrac></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\frac {1}{x_{1}}}{dan}{\frac {1}{x_{2}}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30c87b802ce51e3a0e6d187cfeac0d6d49801458" style="border: 0px; display: inline-block; height: 5.509ex; vertical-align: -2.171ex; width: 10.281ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle cx^{2}+bx+a=0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>�</mi><mi>�</mi><mo>+</mo><mi>�</mi><mo>=</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle cx^{2}+bx+a=0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53c8e0aeff155727a9dcd2529b7294d66eb5bc42" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.505ex; width: 16.89ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle -x_{1}{dan}-x_{2}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>−</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mi>�</mi><mi>�</mi></mrow><mo>−</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub></mstyle></mrow></semantics></math></span><img alt="{\displaystyle -x_{1}{dan}-x_{2}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/abca19f540fbc1b8e303d773aaa291c1686d5289" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 13.257ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ax^{2}-bx+c=0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−</mo><mi>�</mi><mi>�</mi><mo>+</mo><mi>�</mi><mo>=</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ax^{2}-bx+c=0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5624769208dc3463f7fd1d8d03ca2d622e9ce80c" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.505ex; width: 16.89ex;" /></span></td></tr></tbody></table><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Pembuktian_rumus_persamaan_kuadrat">Pembuktian rumus persamaan kuadrat</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&veaction=edit&section=4" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Pembuktian rumus persamaan kuadrat">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&action=edit&section=4" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Pembuktian rumus persamaan kuadrat">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><p style="margin: 0.5em 0px 1em;">Dari bentuk umum persamaan kuadrat,</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ax^{2}+bx+c=0\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>�</mi><mi>�</mi><mo>+</mo><mi>�</mi><mo>=</mo><mn>0</mn><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ax^{2}+bx+c=0\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d0181fd7c4ee9e4d199c21bebf3e056ce2f1be7" style="border: 0px; display: inline-block; height: 2.843ex; margin-right: -0.387ex; vertical-align: -0.505ex; width: 17.277ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">bagi kedua ruas untuk mendapatkan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle a=1}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><mn>1</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle a=1}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6104442ed30596ef4d7795d3186273f68d796ea4" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 5.491ex;" /></span></p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x^{2}+{\frac {b}{a}}x+{\frac {c}{a}}=0,\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mi>�</mi><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mo>=</mo><mn>0</mn><mo>,</mo><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x^{2}+{\frac {b}{a}}x+{\frac {c}{a}}=0,\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e56c46441f053776d798f54a86776294cfc8d58" style="border: 0px; display: inline-block; height: 5.343ex; margin-right: -0.387ex; vertical-align: -1.838ex; width: 18.821ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Pindahkan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\frac {c}{a}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\frac {c}{a}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d3c6b95ea11db24e406ab2e567147367a15c6c1" style="border: 0px; display: inline-block; height: 4.676ex; margin: 0px; vertical-align: -1.838ex; width: 2.066ex;" /></span> ke ruas kanan</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x^{2}+{\frac {b}{a}}x=-{\frac {c}{a}}\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mi>�</mi><mo>=</mo><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x^{2}+{\frac {b}{a}}x=-{\frac {c}{a}}\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b19b880dc605674647a800ce201dc1823435a736" style="border: 0px; display: inline-block; height: 5.343ex; margin-right: -0.387ex; vertical-align: -1.838ex; width: 15.98ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">sehingga teknik melengkapkan kuadrat bisa digunakan di ruas kiri.</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \left(x+{\frac {b}{2a}}\right)^{2}-{\frac {b^{2}}{4a^{2}}}=-{\frac {c}{a}}\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow><mo>(</mo><mrow><mi>�</mi><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mrow><mn>4</mn><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo>=</mo><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \left(x+{\frac {b}{2a}}\right)^{2}-{\frac {b^{2}}{4a^{2}}}=-{\frac {c}{a}}\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/406c4cb788517a82ed362dc8e13ea2e7ea95ddcf" style="border: 0px; display: inline-block; height: 6.509ex; margin-right: -0.387ex; vertical-align: -2.505ex; width: 26.357ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Pindahkan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle -{\frac {b^{2}}{4ac}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mrow><mn>4</mn><mi>�</mi><mi>�</mi></mrow></mfrac></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle -{\frac {b^{2}}{4ac}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/372ed5bcc7c361cbc61b64c7db2b956b07afe65b" style="border: 0px; display: inline-block; height: 5.676ex; margin: 0px; vertical-align: -1.838ex; width: 6.043ex;" /></span> ke ruas kanan</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \left(x+{\frac {b}{2a}}\right)^{2}={\frac {b^{2}}{4a^{2}}}-{\frac {c}{a}}\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow><mo>(</mo><mrow><mi>�</mi><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mrow><mn>4</mn><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \left(x+{\frac {b}{2a}}\right)^{2}={\frac {b^{2}}{4a^{2}}}-{\frac {c}{a}}\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81368e634f8a2aad7be8a39047b9d2e0ef4b5d47" style="border: 0px; display: inline-block; height: 6.509ex; margin-right: -0.387ex; vertical-align: -2.505ex; width: 24.548ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">lalu samakan penyebut di ruas kanan.</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \left(x+{\frac {b}{2a}}\right)^{2}={\frac {b^{2}-4ac}{4a^{2}}}\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow><mo>(</mo><mrow><mi>�</mi><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−</mo><mn>4</mn><mi>�</mi><mi>�</mi></mrow><mrow><mn>4</mn><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \left(x+{\frac {b}{2a}}\right)^{2}={\frac {b^{2}-4ac}{4a^{2}}}\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21b1bc8a1d85065f2b1b15fa3001c4fa80e224b1" style="border: 0px; display: inline-block; height: 6.509ex; margin-right: -0.387ex; vertical-align: -2.505ex; width: 24.487ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Kedua ruas diakar (dipangkatkan setengah), sehingga tanda kuadrat di ruas kiri hilang, dan muncul tanda plus-minus di ruas kanan.</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x+{\frac {b}{2a}}=\pm {\frac {\sqrt {b^{2}-4ac\ }}{2a}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow><mo>=</mo><mo>±</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msqrt><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−</mo><mn>4</mn><mi>�</mi><mi>�</mi><mtext> </mtext></msqrt><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x+{\frac {b}{2a}}=\pm {\frac {\sqrt {b^{2}-4ac\ }}{2a}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91523160e0d8f4b81a584154754f3d1f46beda6a" style="border: 0px; display: inline-block; height: 6.176ex; vertical-align: -1.838ex; width: 24.337ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Pindahkan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle -{\frac {b}{2a}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle -{\frac {b}{2a}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fcda5de4a3cf20ebc76c43543eea248071319e5f" style="border: 0px; display: inline-block; height: 5.343ex; margin: 0px; vertical-align: -1.838ex; width: 5.037ex;" /></span> ke ruas kanan</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x=-{\frac {b}{2a}}\pm {\frac {\sqrt {b^{2}-4ac\ }}{2a}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow><mo>±</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msqrt><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−</mo><mn>4</mn><mi>�</mi><mi>�</mi><mtext> </mtext></msqrt><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x=-{\frac {b}{2a}}\pm {\frac {\sqrt {b^{2}-4ac\ }}{2a}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5999465b793cff05e4bfd1d38c9bb577522124d1" style="border: 0px; display: inline-block; height: 6.176ex; vertical-align: -1.838ex; width: 24.337ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">sehingga didapat rumus kuadrat</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1,2}={\frac {-b\pm {\sqrt {b^{2}-4ac\ }}}{2a}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mo>−</mo><mi>�</mi><mo>±</mo><mrow class="MJX-TeXAtom-ORD"><msqrt><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−</mo><mn>4</mn><mi>�</mi><mi>�</mi><mtext> </mtext></msqrt></mrow></mrow><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1,2}={\frac {-b\pm {\sqrt {b^{2}-4ac\ }}}{2a}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41ec504e72005c70da117bc058b8550ac8fb2122" style="border: 0px; display: inline-block; height: 6.176ex; vertical-align: -1.838ex; width: 24.44ex;" /></span> atau <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1,2}={\frac {-b\pm {\sqrt {D}}}{2a}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mo>−</mo><mi>�</mi><mo>±</mo><mrow class="MJX-TeXAtom-ORD"><msqrt><mi>�</mi></msqrt></mrow></mrow><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1,2}={\frac {-b\pm {\sqrt {D}}}{2a}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ff47b21ea15fc56c01ddd61c15dfee1bac73d2c" style="border: 0px; display: inline-block; height: 5.843ex; vertical-align: -1.838ex; width: 17.104ex;" /></span></dd></dl><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span id="Diskriminan.2Fdeterminan"></span><span class="mw-headline" id="Diskriminan/determinan">Diskriminan/determinan</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&veaction=edit&section=5" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Diskriminan/determinan">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&action=edit&section=5" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Diskriminan/determinan">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><figure class="mw-default-size" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Diskriminan.png" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img class="mw-file-element" data-file-height="417" data-file-width="391" decoding="async" height="235" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Diskriminan.png/220px-Diskriminan.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Diskriminan.png/330px-Diskriminan.png 1.5x, //upload.wikimedia.org/wikipedia/commons/d/d4/Diskriminan.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="220" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Akar-akar dan nilai D.</figcaption></figure><p style="margin: 0.5em 0px 1em;">Dalam rumus kuadrat di atas, terdapat istilah yang berada dalam tanda akar:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle b^{2}-4ac,\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−</mo><mn>4</mn><mi>�</mi><mi>�</mi><mo>,</mo><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle b^{2}-4ac,\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5fe51368556f77d31a43b90c416021f3f409089" style="border: 0px; display: inline-block; height: 3.009ex; margin-right: -0.387ex; vertical-align: -0.671ex; width: 9.325ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">yang disebut sebagai <i><a href="https://id.wikipedia.org/wiki/Diskriminan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Diskriminan">diskriminan</a></i> atau juga sering disebut <i><a href="https://id.wikipedia.org/wiki/Determinan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Determinan">determinan</a></i> suatu persamaan kuadrat. Kadang dinotasikan dengan huruf <i>D</i>.</p><p style="margin: 0.5em 0px 1em;">Suatu persamaan kuadrat dengan koefisien-koefisien <i>riil</i> dapat memiliki hanya sebuah akar atau dua buah <a href="https://id.wikipedia.org/wiki/Akar" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Akar">akar</a> yang berbeda, di mana akar-akar yang dimaksud dapat berbentuk <a href="https://id.wikipedia.org/wiki/Bilangan_riil" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan riil">bilangan riil</a> atau <a href="https://id.wikipedia.org/wiki/Bilangan_kompleks" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan kompleks">kompleks</a>. Dalam hal ini diskriminan menentukan jumlah dan sifat dari akar-akar persamaan kuadrat. Terdapat tiga kasus yang mungkin:</p><ul style="list-style-image: url("/w/skins/Vector/resources/skins.vector.styles/images/bullet-icon.svg?d4515"); margin: 0.3em 0px 0px 1.6em; padding: 0px;"><li style="margin-bottom: 0.1em;">Jika diskriminan bersifat <a class="new" href="https://id.wikipedia.org/w/index.php?title=Positif&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Positif (halaman belum tersedia)">positif</a>, akan terdapat dua akar berbeda yang kedua-duanya merupakan bilangan riil. Untuk persamaan kuadrat dengan koefisien berupa <a href="https://id.wikipedia.org/wiki/Bilangan_bulat" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan bulat">bilangan bulat</a>, apabila diskriminan merupakan suatu <a class="new" href="https://id.wikipedia.org/w/index.php?title=Kuadrat_sempurna&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Kuadrat sempurna (halaman belum tersedia)">kuadrat sempurna</a>, maka akar-akarnya merupakan <a href="https://id.wikipedia.org/wiki/Bilangan_rasional" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan rasional">bilangan rasional</a>—sebaliknya dapat pula merupakan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Bilangan_irrasional_kuadrat&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan irrasional kuadrat (halaman belum tersedia)">bilangan irrasional kuadrat</a>.</li><li style="margin-bottom: 0.1em;">Jika diskriminan bernilai <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Nol" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Nol">nol</a>, terdapat <a class="new" href="https://id.wikipedia.org/w/index.php?title=Eksak&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Eksak (halaman belum tersedia)">eksak</a> satu akar, dan akar yang dimaksud merupakan bilangan riil. Hal ini kadang disebut sebagai <a class="new" href="https://id.wikipedia.org/w/index.php?title=Akar_ganda&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Akar ganda (halaman belum tersedia)">akar ganda</a>, di mana nilainya adalah:</li></ul><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x=-{\frac {b}{2a}}.\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow><mo>.</mo><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x=-{\frac {b}{2a}}.\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/242becca03d78726f8dec19bf48d0a31e3ca8fee" style="border: 0px; display: inline-block; height: 5.343ex; margin-right: -0.387ex; vertical-align: -1.838ex; width: 10.499ex;" /></span></dd></dl></dd></dl><ul style="list-style-image: url("/w/skins/Vector/resources/skins.vector.styles/images/bullet-icon.svg?d4515"); margin: 0.3em 0px 0px 1.6em; padding: 0px;"><li style="margin-bottom: 0.1em;">Jika diskriminan bernilai <a class="new" href="https://id.wikipedia.org/w/index.php?title=Negatif&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Negatif (halaman belum tersedia)">negatif</a>, <i>tidak</i> terdapat akar riil. Sebagai gantinya, terdapat dua buah akar kompleks (tidak-real), yang satu sama lain merupakan <a href="https://id.wikipedia.org/wiki/Konjugat_kompleks" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Konjugat kompleks">konjugat kompleks</a>:</li></ul><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><table style="font-size: 14px;"><tbody><tr><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{+}={\frac {-b}{2a}}+i\left({\frac {\sqrt {4ac-b^{2}}}{2a}}\right)}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mo>+</mo></mrow></msub><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mo>−</mo><mi>�</mi></mrow><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow><mo>+</mo><mi>�</mi><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msqrt><mn>4</mn><mi>�</mi><mi>�</mi><mo>−</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></msqrt><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow><mo>)</mo></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{+}={\frac {-b}{2a}}+i\left({\frac {\sqrt {4ac-b^{2}}}{2a}}\right)}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fbadb5038eac88b8febae3b1f766141b22274b5" style="border: 0px; display: inline-block; height: 7.509ex; vertical-align: -3.171ex; width: 28.743ex;" /></span></td><td align="center" style="width: 100px;">dan</td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{-}={\frac {-b}{2a}}-i\left({\frac {\sqrt {4ac-b^{2}}}{2a}}\right)}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo></mrow></msub><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mo>−</mo><mi>�</mi></mrow><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow><mo>−</mo><mi>�</mi><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msqrt><mn>4</mn><mi>�</mi><mi>�</mi><mo>−</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></msqrt><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow><mo>)</mo></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{-}={\frac {-b}{2a}}-i\left({\frac {\sqrt {4ac-b^{2}}}{2a}}\right)}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96925b49aa39974ba05ae98242d96fa78b37b3dd" style="border: 0px; display: inline-block; height: 7.509ex; vertical-align: -3.171ex; width: 28.743ex;" /></span></td></tr></tbody></table></dd></dl></dd></dl><p style="margin: 0.5em 0px 1em;">Jadi akar-akar akan berbeda, jika dan hanya jika diskriminan bernilai <a class="new" href="https://id.wikipedia.org/w/index.php?title=Tidak_sama_dengan_nol&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Tidak sama dengan nol (halaman belum tersedia)">tidak sama dengan nol</a>, dan akar-akar akan bersifat riil, jika dan hanya jika diskriminan bernilai <a class="new" href="https://id.wikipedia.org/w/index.php?title=Tidak_negatif&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Tidak negatif (halaman belum tersedia)">tidak negatif</a>.</p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Akar_riil_dan_kompleks">Akar riil dan kompleks</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&veaction=edit&section=6" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Akar riil dan kompleks">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&action=edit&section=6" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Akar riil dan kompleks">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><p style="margin: 0.5em 0px 1em;">Persamaan kuadrat dapat memiliki sebuah akar (akar ganda) atau dua buah akar yang berbeda, yang terakhir ini dapat bersifat riil atau kompleks bergantung dari nilai diskriminannya. Akar-akar persamaan kuadrat dapat pula dipandang sebagai <a class="new" href="https://id.wikipedia.org/w/index.php?title=Titik_potong&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Titik potong (halaman belum tersedia)">titik potongnya</a> dengan sumbu <i>x</i> atau garis <i>y = 0</i>.</p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span id="Titik_potong_dengan_garis_y_.3D_d"></span><span class="mw-headline" id="Titik_potong_dengan_garis_y_=_d">Titik potong dengan garis <i>y = d</i></span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&veaction=edit&section=7" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Titik potong dengan garis y = d">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&action=edit&section=7" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Titik potong dengan garis y = d">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;">Dengan cara pandang ini, rumus persamaan kuadrat dapat digunakan apabila diinginkan untuk mencari titik potong antara suatu persamaan kuadrat (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y_{1}=ax^{2}+bx+c\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>=</mo><mi>�</mi><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>�</mi><mi>�</mi><mo>+</mo><mi>�</mi><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y_{1}=ax^{2}+bx+c\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73835c745b3c2270cc99123846a9431f898b7e50" style="border: 0px; display: inline-block; height: 3.009ex; margin: 0px -0.38ex 0px 0px; vertical-align: -0.671ex; width: 17.914ex;" /></span>) dengan suatu garis mendatar (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y_{2}=d\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>=</mo><mi>�</mi><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y_{2}=d\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c097a47bfd4c601fe82e011ad64ca644c89b83b6" style="border: 0px; display: inline-block; height: 2.509ex; margin: 0px -0.387ex 0px 0px; vertical-align: -0.671ex; width: 6.508ex;" /></span>). Hal ini dapat dilakukan dengan mengurangi persamaan kuadrat tersebut dengan persamaan garis yang titik potong antar keduanya ingin dicari dan menyamakannya dengan nol.</p><p style="margin: 0.5em 0px 1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78a9e37f799bdd8621f4e34e75db19fe08d108bb" style="border: 0px; display: inline-block; height: 0.343ex; margin: 0px 0px 0px -0.387ex; vertical-align: -0.171ex; width: 0.387ex;" /></span></p><p style="margin: 0.5em 0px 1em;">Intepretasi yang sama pun berlaku, yaitu bila:</p><ul style="list-style-image: url("/w/skins/Vector/resources/skins.vector.styles/images/bullet-icon.svg?d4515"); margin: 0.3em 0px 0px 1.6em; padding: 0px;"><li style="margin-bottom: 0.1em;">diskriminan positif, terdapat dua titik potong antara <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y_{1}\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y_{1}\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aaf6f379934a3c3590d2e35285b04f7aaab0e12b" style="border: 0px; display: inline-block; height: 2.009ex; margin-right: -0.387ex; vertical-align: -0.671ex; width: 2.193ex;" /></span> dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y_{2}\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y_{2}\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d102e6a2f38c8d81feacf87c7c5ea55ba1fabe9" style="border: 0px; display: inline-block; height: 2.009ex; margin-right: -0.387ex; vertical-align: -0.671ex; width: 2.193ex;" /></span>,</li><li style="margin-bottom: 0.1em;">diskriminan nol, terdapat hanya satu titik potong antara <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y_{1}\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y_{1}\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aaf6f379934a3c3590d2e35285b04f7aaab0e12b" style="border: 0px; display: inline-block; height: 2.009ex; margin-right: -0.387ex; vertical-align: -0.671ex; width: 2.193ex;" /></span> dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y_{2}\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y_{2}\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d102e6a2f38c8d81feacf87c7c5ea55ba1fabe9" style="border: 0px; display: inline-block; height: 2.009ex; margin-right: -0.387ex; vertical-align: -0.671ex; width: 2.193ex;" /></span>, dan</li><li style="margin-bottom: 0.1em;">diskriminan negatif, tidak terdapat titik potong antara kedua kurva, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y_{1}\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y_{1}\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aaf6f379934a3c3590d2e35285b04f7aaab0e12b" style="border: 0px; display: inline-block; height: 2.009ex; margin-right: -0.387ex; vertical-align: -0.671ex; width: 2.193ex;" /></span> dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y_{2}\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y_{2}\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d102e6a2f38c8d81feacf87c7c5ea55ba1fabe9" style="border: 0px; display: inline-block; height: 2.009ex; margin-right: -0.387ex; vertical-align: -0.671ex; width: 2.193ex;" /></span>.</li></ul><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Nilai-nilai_y">Nilai-nilai <i>y</i></span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&veaction=edit&section=8" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Nilai-nilai y">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&action=edit&section=8" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Nilai-nilai y">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;">Akar-akar suatu persamaan kuadrat menentukan rentang <i>x</i> di mana nilai-nilai <i>y</i> berharga positif atau negatif. Harga-harga ini ditentukan oleh nilai konstanta kuadrat <i>a</i>:</p><table class="wikitable" style="background-color: #f8f9fa; border-collapse: collapse; border: 1px solid rgb(162, 169, 177); color: #202122; font-size: 14px; margin: 1em 0px; text-align: center;"><caption style="font-weight: bold;"><b>Harga-harga <i>y</i></b></caption><tbody><tr><td rowspan="2" style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"></td><td colspan="3" style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle a>0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>></mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle a>0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23c89bcc56938fb3172dd2fb81f128655381b885" style="border: 0px; display: inline-block; height: 2.176ex; margin-right: -0.294ex; vertical-align: -0.338ex; width: 5.398ex;" /></span></td><td colspan="3" style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle a<0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo><</mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle a<0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6827560d7aa6f6af466a9a497f003489f97b4945" style="border: 0px; display: inline-block; height: 2.176ex; margin-right: -0.294ex; vertical-align: -0.338ex; width: 5.398ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x<x_{1}\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo><</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x<x_{1}\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4197b2c0d20848097cf4afe848064991252247f" style="border: 0px; display: inline-block; height: 2.176ex; margin-right: -0.387ex; vertical-align: -0.671ex; width: 6.812ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}<x<x_{2}\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo><</mo><mi>�</mi><mo><</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}<x<x_{2}\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31a7d5fec7729538530918c017d19fa1ebb16abb" style="border: 0px; display: inline-block; height: 2.176ex; margin-right: -0.387ex; vertical-align: -0.671ex; width: 12.294ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x>x_{2}\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>></mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x>x_{2}\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88a0c665789aa70005362f8573f1eab26f9fab2f" style="border: 0px; display: inline-block; height: 2.176ex; margin-right: -0.387ex; vertical-align: -0.671ex; width: 6.812ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x<x_{1}\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo><</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x<x_{1}\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4197b2c0d20848097cf4afe848064991252247f" style="border: 0px; display: inline-block; height: 2.176ex; margin-right: -0.387ex; vertical-align: -0.671ex; width: 6.812ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}<x<x_{2}\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo><</mo><mi>�</mi><mo><</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}<x<x_{2}\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31a7d5fec7729538530918c017d19fa1ebb16abb" style="border: 0px; display: inline-block; height: 2.176ex; margin-right: -0.387ex; vertical-align: -0.671ex; width: 12.294ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x>x_{2}\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>></mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x>x_{2}\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88a0c665789aa70005362f8573f1eab26f9fab2f" style="border: 0px; display: inline-block; height: 2.176ex; margin-right: -0.387ex; vertical-align: -0.671ex; width: 6.812ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle D>0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>></mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle D>0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/837bab831a24c842b720f211c912df66e20c787d" style="border: 0px; display: inline-block; height: 2.176ex; margin-right: -0.294ex; vertical-align: -0.338ex; width: 6.092ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y>0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>></mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y>0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d77c04336cda6f083d2b7a7534de6510274794c" style="border: 0px; display: inline-block; height: 2.509ex; margin-right: -0.294ex; vertical-align: -0.671ex; width: 5.324ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y<0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo><</mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y<0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c55fb38994f01b8c3e4376233e249c895d7f7371" style="border: 0px; display: inline-block; height: 2.509ex; margin-right: -0.294ex; vertical-align: -0.671ex; width: 5.324ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y>0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>></mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y>0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d77c04336cda6f083d2b7a7534de6510274794c" style="border: 0px; display: inline-block; height: 2.509ex; margin-right: -0.294ex; vertical-align: -0.671ex; width: 5.324ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y<0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo><</mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y<0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c55fb38994f01b8c3e4376233e249c895d7f7371" style="border: 0px; display: inline-block; height: 2.509ex; margin-right: -0.294ex; vertical-align: -0.671ex; width: 5.324ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y>0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>></mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y>0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d77c04336cda6f083d2b7a7534de6510274794c" style="border: 0px; display: inline-block; height: 2.509ex; margin-right: -0.294ex; vertical-align: -0.671ex; width: 5.324ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y<0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo><</mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y<0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c55fb38994f01b8c3e4376233e249c895d7f7371" style="border: 0px; display: inline-block; height: 2.509ex; margin-right: -0.294ex; vertical-align: -0.671ex; width: 5.324ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle D=0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle D=0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee46a19727189209055c5eec01983de1da8e42da" style="border: 0px; display: inline-block; height: 2.176ex; margin-right: -0.294ex; vertical-align: -0.338ex; width: 6.092ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y>0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>></mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y>0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d77c04336cda6f083d2b7a7534de6510274794c" style="border: 0px; display: inline-block; height: 2.509ex; margin-right: -0.294ex; vertical-align: -0.671ex; width: 5.324ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle -\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>−</mo><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle -\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c600310a29191433c0b2c83d95b9e15e7fed3f52" style="border: 0px; display: inline-block; height: 2.176ex; margin-right: -0.192ex; vertical-align: -0.505ex; width: 1.613ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y>0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>></mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y>0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d77c04336cda6f083d2b7a7534de6510274794c" style="border: 0px; display: inline-block; height: 2.509ex; margin-right: -0.294ex; vertical-align: -0.671ex; width: 5.324ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y<0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo><</mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y<0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c55fb38994f01b8c3e4376233e249c895d7f7371" style="border: 0px; display: inline-block; height: 2.509ex; margin-right: -0.294ex; vertical-align: -0.671ex; width: 5.324ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle -\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>−</mo><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle -\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c600310a29191433c0b2c83d95b9e15e7fed3f52" style="border: 0px; display: inline-block; height: 2.176ex; margin-right: -0.192ex; vertical-align: -0.505ex; width: 1.613ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y<0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo><</mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y<0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c55fb38994f01b8c3e4376233e249c895d7f7371" style="border: 0px; display: inline-block; height: 2.509ex; margin-right: -0.294ex; vertical-align: -0.671ex; width: 5.324ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle D<0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo><</mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle D<0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c97d0b81ab7b1a30d2aa6ea6b6f43348a217b8d2" style="border: 0px; display: inline-block; height: 2.176ex; margin-right: -0.294ex; vertical-align: -0.338ex; width: 6.092ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y>0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>></mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y>0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d77c04336cda6f083d2b7a7534de6510274794c" style="border: 0px; display: inline-block; height: 2.509ex; margin-right: -0.294ex; vertical-align: -0.671ex; width: 5.324ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle -\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>−</mo><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle -\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c600310a29191433c0b2c83d95b9e15e7fed3f52" style="border: 0px; display: inline-block; height: 2.176ex; margin-right: -0.192ex; vertical-align: -0.505ex; width: 1.613ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y>0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>></mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y>0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d77c04336cda6f083d2b7a7534de6510274794c" style="border: 0px; display: inline-block; height: 2.509ex; margin-right: -0.294ex; vertical-align: -0.671ex; width: 5.324ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y<0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo><</mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y<0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c55fb38994f01b8c3e4376233e249c895d7f7371" style="border: 0px; display: inline-block; height: 2.509ex; margin-right: -0.294ex; vertical-align: -0.671ex; width: 5.324ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle -\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>−</mo><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle -\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c600310a29191433c0b2c83d95b9e15e7fed3f52" style="border: 0px; display: inline-block; height: 2.176ex; margin-right: -0.192ex; vertical-align: -0.505ex; width: 1.613ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y<0\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo><</mo><mn>0</mn><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y<0\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c55fb38994f01b8c3e4376233e249c895d7f7371" style="border: 0px; display: inline-block; height: 2.509ex; margin-right: -0.294ex; vertical-align: -0.671ex; width: 5.324ex;" /></span></td></tr></tbody></table><p style="margin: 0.5em 0px 1em;">dengan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}<x_{2}\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo><</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}<x_{2}\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f08845929d54300e56597e902a202abce59ba51" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px -0.387ex 0px 0px; vertical-align: -0.671ex; width: 7.866ex;" /></span> merupakan akar-akar persamaan kuadrat. Dalam tabel di atas, apabila <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x,x_{1},x_{2}\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>,</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x,x_{1},x_{2}\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56b51a3e052c316d47b2cefc744675d36c48e687" style="border: 0px; display: inline-block; height: 2.009ex; margin: 0px -0.387ex 0px 0px; vertical-align: -0.671ex; width: 8.165ex;" /></span> bersifat kompleks, maka yang dimaksud adalah <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \Re \ x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi mathvariant="normal">ℜ</mi><mtext> </mtext><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \Re \ x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/012297c414a732811766d5ce1ae1f25cc8414aec" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 3.835ex;" /></span> (nilai riil)-nya.</p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Geometri">Geometri</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&veaction=edit&section=9" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Geometri">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&action=edit&section=9" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Geometri">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><figure class="mw-halign-right" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Polynomialdeg2.png" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img class="mw-file-element" data-file-height="179" data-file-width="233" decoding="async" height="154" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/14/Polynomialdeg2.png/200px-Polynomialdeg2.png" srcset="//upload.wikimedia.org/wikipedia/commons/1/14/Polynomialdeg2.png 1.5x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="200" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Untuk <a href="https://id.wikipedia.org/wiki/Fungsi_kuadrat" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi kuadrat">fungsi kuadrat</a>:<br /><i>f</i>(<i>x</i>) = <i>x</i><sup style="font-size: 9.9008px; line-height: 1;">2</sup> − <i>x</i> − 2 = (<i>x</i> + 1)(<i>x</i> − 2), dengan variabel <i>x</i> adalah <a href="https://id.wikipedia.org/wiki/Bilangan_riil" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan riil">bilangan riil</a>. <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Koordinat" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Koordinat">koordinat</a>-<i>x</i> dari titik-titik di mana kurva menyentuh sumbu-<i>x</i>, <i>x</i> = −1 dan <i>x</i> = 2, adalah <a href="https://id.wikipedia.org/wiki/Akar" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Akar">akar-akar</a> dari persamaan kuadrat: <i>x</i><sup style="font-size: 9.9008px; line-height: 1;">2</sup> − <i>x</i> − 2 = 0.</figcaption></figure><p style="margin: 0.5em 0px 1em;">Akar-akar dari persamaan kuadrat adalah juga <a class="new" href="https://id.wikipedia.org/w/index.php?title=Pembuat_nol&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Pembuat nol (halaman belum tersedia)">pembuat nol</a> dari fungsi kuadrat tersebut:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f(x)=ax^{2}+bx+c,\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><mi>�</mi><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>�</mi><mi>�</mi><mo>+</mo><mi>�</mi><mo>,</mo><mspace width="thinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f(x)=ax^{2}+bx+c,\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47b41b378e71c8a3848dd2e283ce3c096f5f108c" style="border: 0px; display: inline-block; height: 3.176ex; vertical-align: -0.838ex; width: 21.179ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">dikarenakan akar-akar tersebut merupakan nilai <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec21bb206c6c9f458130ab7ffddfe3fd8d0fa6bb" style="border: 0px; display: inline-block; height: 1.676ex; margin: 0px -0.387ex 0px 0px; vertical-align: -0.338ex; width: 1.717ex;" /></span> yang memberikan</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f(x)=0.\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0.</mn><mspace width="thinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f(x)=0.\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b3e0937afb27608488b3b712b23f35657a63e22" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.838ex; width: 9.712ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Jika <i>a</i>, <i>b</i>, dan <i>c</i> adalah <a href="https://id.wikipedia.org/wiki/Bilangan_riil" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan riil">bilangan riil</a>, dan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Domain" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Domain">domain</a> dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7332b398fc3123f27b3dd16dd4590573ccd2f4a7" style="border: 0px; display: inline-block; height: 2.509ex; margin: 0px -0.387ex 0px 0px; vertical-align: -0.671ex; width: 1.666ex;" /></span> adalah himpunan bilangan riil, maka pembuat nol dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f\,\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mspace width="thinmathspace"></mspace><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f\,\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7332b398fc3123f27b3dd16dd4590573ccd2f4a7" style="border: 0px; display: inline-block; height: 2.509ex; margin: 0px -0.387ex 0px 0px; vertical-align: -0.671ex; width: 1.666ex;" /></span> adalah eksak <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Koordinat" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Koordinat">koordinat</a>-<i>x</i> di saat titik-titik tersebut menyentuh <a class="new" href="https://id.wikipedia.org/w/index.php?title=Sumbu-x&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Sumbu-x (halaman belum tersedia)">sumbu-x</a>.</p><p style="margin: 0.5em 0px 1em;">Mengikuti pernyataan di atas, bahwa jika diskriminan berharga positif, <a href="https://id.wikipedia.org/wiki/Kurva" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kurva">kurva</a> persamaan kuadrat akan menyentuh sumbu-x pada dua buah titik (dua buah <a class="new" href="https://id.wikipedia.org/w/index.php?title=Titik_potong&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Titik potong (halaman belum tersedia)">titik potong</a>), jika berharga nol, akan menyentuh di satu titik dan jika berharga negatif, kurva tidak akan menyentuh sumbu-x.</p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Rumus_fungsi_kuadrat">Rumus fungsi kuadrat</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&veaction=edit&section=10" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Rumus fungsi kuadrat">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&action=edit&section=10" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Rumus fungsi kuadrat">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><p style="margin: 0.5em 0px 1em;">Persamaan fungsi kuadrat: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f(x)=ax^{2}+bx+c\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><mi>�</mi><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>�</mi><mi>�</mi><mo>+</mo><mi>�</mi><mspace width="thinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f(x)=ax^{2}+bx+c\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b9584ac5ad8195bc3fbfabfa0e07d4c77a8f8bd" style="border: 0px; display: inline-block; height: 3.176ex; margin: 0px; vertical-align: -0.838ex; width: 20.532ex;" /></span> dimana f(x) = y maka titik balik (harga ekstrem/titik puncak) fungsi kuadrat adalah (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle -{\frac {b}{2a}}\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow><mspace width="thinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle -{\frac {b}{2a}}\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d7b10f76dfcc4d9b6f1c53759d9004766487001" style="border: 0px; display: inline-block; height: 5.343ex; margin: 0px; vertical-align: -1.838ex; width: 5.424ex;" /></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle -{\frac {D}{4a}}\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>4</mn><mi>�</mi></mrow></mfrac></mrow><mspace width="thinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle -{\frac {D}{4a}}\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7947534774b1b9bf3bd011b8c57bdac24be659d9" style="border: 0px; display: inline-block; height: 5.176ex; margin: 0px; vertical-align: -1.838ex; width: 5.424ex;" /></span>).</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dt style="font-weight: bold; margin-bottom: 0.1em;">Pembuktian</dt><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"></dd></dl><p style="margin: 0.5em 0px 1em;">Dari bentuk umum persamaan kuadrat,</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ax^{2}+bx+c=y\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>�</mi><mi>�</mi><mo>+</mo><mi>�</mi><mo>=</mo><mi>�</mi><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ax^{2}+bx+c=y\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2afda54c8b3479f00726bfabae78504816d991c2" style="border: 0px; display: inline-block; height: 3.009ex; margin-right: -0.387ex; vertical-align: -0.671ex; width: 16.883ex;" /></span></dd></dl><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle a(x^{2}+{\frac {b}{a}}x+{\frac {c}{a}})=y\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mi>�</mi><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mo stretchy="false">)</mo><mo>=</mo><mi>�</mi><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle a(x^{2}+{\frac {b}{a}}x+{\frac {c}{a}})=y\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/809defb433405e3901184f4bd71d6a6313b8e822" style="border: 0px; display: inline-block; height: 5.343ex; margin-right: -0.387ex; vertical-align: -1.838ex; width: 20.819ex;" /></span></dd></dl><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle a(\left(x+{\frac {b}{2a}}\right)^{2}-{\frac {b^{2}}{4a^{2}}}+{\frac {c}{a}})=y\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><msup><mrow><mo>(</mo><mrow><mi>�</mi><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mrow><mn>4</mn><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mo stretchy="false">)</mo><mo>=</mo><mi>�</mi><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle a(\left(x+{\frac {b}{2a}}\right)^{2}-{\frac {b^{2}}{4a^{2}}}+{\frac {c}{a}})=y\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74d046619d7d19e69af076a03e0b37e449f19b70" style="border: 0px; display: inline-block; height: 6.509ex; margin-right: -0.387ex; vertical-align: -2.505ex; width: 31.196ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">anggapan bahwa <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle (x+{\frac {b}{2a}})^{2}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">(</mo><mi>�</mi><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle (x+{\frac {b}{2a}})^{2}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e54c35a743f8d8b81a6b0a751dcdfddbcbce79a8" style="border: 0px; display: inline-block; height: 5.343ex; margin: 0px; vertical-align: -1.838ex; width: 10.262ex;" /></span> adalah 0 maka:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle (x+{\frac {b}{2a}})^{2}=0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">(</mo><mi>�</mi><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>=</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle (x+{\frac {b}{2a}})^{2}=0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ca7bda2956310b4b15fd489615130895b0f024a" style="border: 0px; display: inline-block; height: 5.343ex; vertical-align: -1.838ex; width: 14.523ex;" /></span></dd></dl><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x=-{\frac {b}{2a}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x=-{\frac {b}{2a}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/149700f11980672ab7e1d5af4898f0ac67aba29b" style="border: 0px; display: inline-block; height: 5.343ex; vertical-align: -1.838ex; width: 9.465ex;" /></span></dd></dl><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle a(-{\frac {b^{2}}{4a^{2}}}+{\frac {c}{a}})=y\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mrow><mn>4</mn><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mo stretchy="false">)</mo><mo>=</mo><mi>�</mi><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle a(-{\frac {b^{2}}{4a^{2}}}+{\frac {c}{a}})=y\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ef042b3ac32e1796b3c68d5fd854cf4c8706b5d" style="border: 0px; display: inline-block; height: 6.009ex; margin-right: -0.387ex; vertical-align: -2.171ex; width: 18.29ex;" /></span></dd></dl><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle a(-{\frac {b^{2}}{4a^{2}}}+{\frac {4ac}{a^{2}}})=y\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mrow><mn>4</mn><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mn>4</mn><mi>�</mi><mi>�</mi></mrow><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mfrac></mrow><mo stretchy="false">)</mo><mo>=</mo><mi>�</mi><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle a(-{\frac {b^{2}}{4a^{2}}}+{\frac {4ac}{a^{2}}})=y\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7be5ac7bb66d4a747fe3f3ce6e8a2d9659bd07c6" style="border: 0px; display: inline-block; height: 6.009ex; margin-right: -0.387ex; vertical-align: -2.171ex; width: 20.459ex;" /></span></dd></dl><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle -{\frac {b^{2}-4ac}{4a}}=y\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−</mo><mn>4</mn><mi>�</mi><mi>�</mi></mrow><mrow><mn>4</mn><mi>�</mi></mrow></mfrac></mrow><mo>=</mo><mi>�</mi><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle -{\frac {b^{2}-4ac}{4a}}=y\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f8cd4ffef9aa0f1e4f1835e517bbbb143aee813" style="border: 0px; display: inline-block; height: 5.676ex; margin-right: -0.387ex; vertical-align: -1.838ex; width: 15.19ex;" /></span> atau <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle -{\frac {D}{4a}}=y\!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>4</mn><mi>�</mi></mrow></mfrac></mrow><mo>=</mo><mi>�</mi><mspace width="negativethinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle -{\frac {D}{4a}}=y\!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dee7433d4485882cd1a7c814d598d012038eccb8" style="border: 0px; display: inline-block; height: 5.176ex; margin-right: -0.387ex; vertical-align: -1.838ex; width: 9.29ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">maka titik balik adalah (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle -{\frac {b}{2a}}\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow><mspace width="thinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle -{\frac {b}{2a}}\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d7b10f76dfcc4d9b6f1c53759d9004766487001" style="border: 0px; display: inline-block; height: 5.343ex; margin: 0px; vertical-align: -1.838ex; width: 5.424ex;" /></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle -{\frac {D}{4a}}\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>4</mn><mi>�</mi></mrow></mfrac></mrow><mspace width="thinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle -{\frac {D}{4a}}\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7947534774b1b9bf3bd011b8c57bdac24be659d9" style="border: 0px; display: inline-block; height: 5.176ex; margin: 0px; vertical-align: -1.838ex; width: 5.424ex;" /></span>).</p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Topik_lanjutan">Topik lanjutan</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&veaction=edit&section=11" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Topik lanjutan">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&action=edit&section=11" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Topik lanjutan">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Metode_alternatif_penghitungan_akar">Metode alternatif penghitungan akar</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&veaction=edit&section=12" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Metode alternatif penghitungan akar">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&action=edit&section=12" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Metode alternatif penghitungan akar">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><h4 style="color: black; font-size: 14px; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Rumus_Vieta">Rumus Vieta</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&veaction=edit&section=13" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Rumus Vieta">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&action=edit&section=13" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Rumus Vieta">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h4><div class="hatnote navigation-not-searchable" role="note" style="font-style: italic; margin-bottom: 0.5em; padding-left: 1.6em;">Artikel utama: <a href="https://id.wikipedia.org/wiki/Rumus_Vieta" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Rumus Vieta">Rumus Vieta</a></div><figure style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Excel_quadratic_error.PNG" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img alt="Gambar 5. Grafik perbedaan antara pendekatan Vieta untuk akar persamaan kuadrat yang lebih kecil x kuadrat plus b x plus c sama dengan nol dibandingkan dengan nilai yang dihitung menggunakan rumus kuadrat. Selisihnya diplot sebagai fungsi dari b untuk dua nilai c yang berbeda, c sama dengan 4, dan c sama dengan 400.000. Grafik adalah grafik log log, dengan sumbu vertikal, perbedaannya, mulai dari sepuluh hingga. Sumbu horizontal, b, berkisar dari 10 di kiri hingga sepuluh hingga kedelapan di kanan. Pendekatan Vieta untuk akar yang lebih kecil tidak akurat untuk b kecil tetapi akurat untuk b besar. Evaluasi langsung dari akar yang lebih kecil menggunakan rumus kuadrat akurat untuk b kecil dengan nilai akar yang sebanding, tetapi mengalami hilangnya kesalahan signifikansi untuk b besar dan spasi lebar. Ketika c sama dengan 4, pendekatan Vieta dimulai dengan buruk di sebelah kiri, tetapi menjadi lebih baik dengan b yang lebih besar, perbedaan antara pendekatan Vieta dan rumus kuadrat mencapai minimum pada perkiraan. Perkiraan Vieta dan rumus kuadrat kemudian mulai divergen lagi karena rumus kuadrat mengalami error loss of signifikan. Jika c sama dengan empat ratus ribu, perbedaan antara pendekatan Vieta dan rumus kuadrat mencapai minimum pada kira-kira b sama dengan sepuluh pangkat tujuh. Kedua kurva tersebut lurus ke kiri minimum, menunjukkan hubungan kekuatan monomial sederhana antara selisih dan b. Demikian juga, kedua kurva tersebut kira-kira lurus ke kanan minimum, yang menunjukkan hubungan kekuatan, kecuali bahwa garis lurus memiliki coretan di dalamnya karena hilangnya signifikansi" class="mw-file-element" data-file-height="364" data-file-width="685" decoding="async" height="186" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/53/Excel_quadratic_error.PNG/350px-Excel_quadratic_error.PNG" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Excel_quadratic_error.PNG/525px-Excel_quadratic_error.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/5/53/Excel_quadratic_error.PNG 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="350" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Gambar 5. Grafik perbedaan antara pendekatan Vieta untuk akar persamaan kuadrat yang lebih kecil <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>x</i><sup style="font-size: 11.6829px; line-height: 1;">2</sup> + <i>bx</i> + <i>c</i> = 0</span> dibandingkan dengan nilai yang dihitung menggunakan rumus kuadrat. Perkiraan Vieta tidak akurat untuk yang kecil <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i></span> tetapi akurat untuk ukuran besar <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i></span>. Evaluasi langsung menggunakan rumus kuadrat akurat untuk yang kecil <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i></span> dengan akar dari nilai yang sebanding tetapi mengalami hilangnya kesalahan signifikansi yang besar <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i></span> dan akar berjarak lebar. Perbedaan antara perkiraan Vieta <i>versus</i> penghitungan langsung mencapai minimum pada titik-titik besar, dan pembulatan menyebabkan coretan di kurva melebihi minimum ini.</figcaption></figure><p style="margin: 0.5em 0px 1em;"><a href="https://id.wikipedia.org/wiki/Rumus_Vieta" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Rumus Vieta">Rumus Vieta</a> memberikan hubungan sederhana antara akar polinomial dan koefisiennya. Dalam kasus polinomial kuadrat, mereka mengambil bentuk berikut:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}+x_{2}=-{\frac {b}{a}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>=</mo><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}+x_{2}=-{\frac {b}{a}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62332ad46f539c2a729aed1059d4b5f1cb0c4b1a" style="border: 0px; display: inline-block; height: 5.343ex; vertical-align: -1.838ex; width: 14.581ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">dan</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}x_{2}={\frac {c}{a}}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}x_{2}={\frac {c}{a}}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18ac705f6c2adb1be013b1f79a734964d265f2ae" style="border: 0px; display: inline-block; height: 4.676ex; vertical-align: -1.838ex; width: 10.579ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Hasil ini langsung mengikuti dari relasi:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \left(x-x_{1}\right)\left(x-x_{2}\right)=x^{2}-\left(x_{1}+x_{2}\right)x+x_{1}x_{2}=0,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow><mo>(</mo><mrow><mi>�</mi><mo>−</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mi>�</mi><mo>−</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub></mrow><mo>)</mo></mrow><mo>=</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−</mo><mrow><mo>(</mo><mrow><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub></mrow><mo>)</mo></mrow><mi>�</mi><mo>+</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>,</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \left(x-x_{1}\right)\left(x-x_{2}\right)=x^{2}-\left(x_{1}+x_{2}\right)x+x_{1}x_{2}=0,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf3a4d5efda75679777a8c129b5de9489064adb4" style="border: 0px; display: inline-block; height: 3.176ex; vertical-align: -0.838ex; width: 49.087ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">yang dapat dibandingkan istilah demi istilah dengan</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x^{2}+(b/a)x+c/a=0.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mo stretchy="false">(</mo><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>�</mi><mo stretchy="false">)</mo><mi>�</mi><mo>+</mo><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>�</mi><mo>=</mo><mn>0.</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x^{2}+(b/a)x+c/a=0.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8078d62c198aaf6d891fb2e084478684df59c7e8" style="border: 0px; display: inline-block; height: 3.176ex; vertical-align: -0.838ex; width: 22.9ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Rumus pertama di atas menghasilkan ekspresi yang sesuai saat membuat grafik fungsi kuadrat. Karena grafiknya simetris terhadap garis vertikal melalui <a href="https://id.wikipedia.org/wiki/Fungsi_kuadrat#Puncak" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi kuadrat">simpul</a>, ketika ada dua akar nyata, koordinat <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>x</i></span> titik koordinat terletak di av. Jadi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>x</i></span> koordinat dari simpul diberikan oleh ekspresi</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{V}={\frac {x_{1}+x_{2}}{2}}=-{\frac {b}{2a}}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub></mrow><mn>2</mn></mfrac></mrow><mo>=</mo><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>2</mn><mi>�</mi></mrow></mfrac></mrow><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{V}={\frac {x_{1}+x_{2}}{2}}=-{\frac {b}{2a}}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0e68afcb918e5c7f72267945b801f53e68aaddd" style="border: 0px; display: inline-block; height: 5.343ex; vertical-align: -1.838ex; width: 23.15ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;"><span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>y</i></span> koordinat dapat diperoleh dengan mensubstitusi hasil di atas ke dalam persamaan kuadrat yang diberikan, memberikan</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y_{V}=-{\frac {b^{2}}{4a}}+c=-{\frac {b^{2}-4ac}{4a}}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo>=</mo><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mrow><mn>4</mn><mi>�</mi></mrow></mfrac></mrow><mo>+</mo><mi>�</mi><mo>=</mo><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−</mo><mn>4</mn><mi>�</mi><mi>�</mi></mrow><mrow><mn>4</mn><mi>�</mi></mrow></mfrac></mrow><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y_{V}=-{\frac {b^{2}}{4a}}+c=-{\frac {b^{2}-4ac}{4a}}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d988abbaca5bdf63417d24a5eb218670c0be61bc" style="border: 0px; display: inline-block; height: 5.676ex; vertical-align: -1.838ex; width: 29.298ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Sebagai masalah praktis, rumus Vieta menyediakan metode yang berguna untuk menemukan <a href="https://id.wikipedia.org/wiki/Akar_kuadrat" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Akar kuadrat">akar kuadrat</a> dalam kasus di mana satu akar jauh lebih kecil dari yang lain. Bila <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">| <i>x</i> <sub style="font-size: 13.216px; line-height: 1;">2</sub>| << | <i>x</i> <sub style="font-size: 13.216px; line-height: 1;">1</sub>|</span>, maka <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>x</i> <sub style="font-size: 13.216px; line-height: 1;">1</sub> + <i>x</i> <sub style="font-size: 13.216px; line-height: 1;">2</sub> ≈ <i>x</i> <sub style="font-size: 13.216px; line-height: 1;">1</sub></span>, dan kami memiliki perkiraan:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}\approx -{\frac {b}{a}}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>≈</mo><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}\approx -{\frac {b}{a}}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/597d8233434bd192fec87f4d6f2654b28229b3f3" style="border: 0px; display: inline-block; height: 5.343ex; vertical-align: -1.838ex; width: 10.003ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Rumus Vieta kedua kemudian memberikan:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{2}={\frac {c}{ax_{1}}}\approx -{\frac {c}{b}}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mi>�</mi><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub></mrow></mfrac></mrow><mo>≈</mo><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{2}={\frac {c}{ax_{1}}}\approx -{\frac {c}{b}}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d832e4efa38d40e6f52e578875f3662529b7ac4" style="border: 0px; display: inline-block; height: 5.009ex; vertical-align: -2.171ex; width: 17.329ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Rumus-rumus ini jauh lebih mudah untuk dievaluasi daripada rumus kuadrat dengan syarat satu akar besar dan satu akar kecil, karena rumus kuadrat mengevaluasi akar kecil sebagai selisih <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i></span>), yang menyebabkan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Kesalahan_pembulatan&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Kesalahan pembulatan (halaman belum tersedia)">kesalahan pembulatan</a> dalam evaluasi numerik. Gambar 5 menunjukkan perbedaan antara (i) evaluasi langsung menggunakan rumus kuadrat (akurat ketika akar memiliki nilai yang berdekatan) dan (ii) evaluasi berdasarkan perkiraan rumus Vieta di atas (akurat ketika akar berjarak lebar). Sebagai koefisien linear <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i></span> meningkat, awalnya rumus kuadrat akurat, dan rumus perkiraan meningkatkan keakuratannya, yang mengarah ke perbedaan yang lebih kecil antara metode sebagai <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i></span> meningkat. Namun, pada titik tertentu rumus kuadrat mulai kehilangan akurasinya karena kesalahan pembulatan, sedangkan metode perkiraan terus ditingkatkan. Akibatnya, perbedaan antara metode-metode tersebut mulai meningkat karena rumus kuadrat menjadi semakin buruk.</p><p style="margin: 0.5em 0px 1em;">Situasi ini umumnya muncul dalam desain amplifier, di mana akar yang terpisah jauh diinginkan untuk memastikan operasi yang stabil (lihat <a class="new" href="https://id.wikipedia.org/w/index.php?title=Respons_langkah&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Respons langkah (halaman belum tersedia)">respons langkah</a>).</p><h4 style="color: black; font-size: 14px; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Solusi_trigonometri">Solusi trigonometri</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&veaction=edit&section=14" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Solusi trigonometri">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&action=edit&section=14" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Solusi trigonometri">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h4><p style="margin: 0.5em 0px 1em;">Pada hari-hari sebelum kalkulator, orang akan menggunakan <a href="https://id.wikipedia.org/wiki/Tabel_matematika" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Tabel matematika">tabel matematika</a> daftar angka yang menunjukkan hasil kalkulasi dengan berbagai argumen untuk menyederhanakan dan mempercepat. Tabel logaritma dan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Fungsi_trigonometrik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi trigonometrik">fungsi trigonometri</a> biasa ditemukan dalam buku teks matematika dan sains. Tabel khusus diterbitkan untuk aplikasi seperti astronomi, navigasi angkasa, dan statistik. Ada metode perkiraan numerik, yang disebut <a class="new" href="https://id.wikipedia.org/w/index.php?title=Prosthaphaeresis&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Prosthaphaeresis (halaman belum tersedia)">prosthaphaeresis</a>, yang menawarkan jalan pintas di sekitar operasi yang memakan waktu seperti perkalian dan pengambilan kekuatan dan akar.<sup class="reference" id="cite_ref-Ballew2007_1-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Persamaan_kuadrat#cite_note-Ballew2007-1" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[1]</a></sup> Para astronom, khususnya, prihatin dengan metode yang dapat mempercepat rangkaian panjang penghitungan yang terlibat dalam penghitungan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Mekanika_angkasa&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Mekanika angkasa (halaman belum tersedia)">mekanika angkasa</a>.</p><p style="margin: 0.5em 0px 1em;">Dalam konteks inilah kita dapat memahami perkembangan cara memecahkan persamaan kuadrat dengan bantuan substitusi trigonometri. Pertimbangkan bentuk alternatif kuadrat berikut,</p><p style="margin: 0.5em 0px 1em;"><b>[1]</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ax^{2}+bx\pm c=0,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>�</mi><mi>�</mi><mo>±</mo><mi>�</mi><mo>=</mo><mn>0</mn><mo>,</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ax^{2}+bx\pm c=0,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab856293ef2070d617fe9096955917c5d5552f10" style="border: 0px; display: inline-block; height: 3.009ex; margin: 0px; vertical-align: -0.671ex; width: 17.536ex;" /></span></p><p style="margin: 0.5em 0px 1em;">dimana lambang ± dipilih sehingga <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>a</i></span> dengan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>c</i></span> mungkin keduanya positif. Dengan mengganti</p><p style="margin: 0.5em 0px 1em;"><b>[2]</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x={\sqrt {c/a}}\tan \theta }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><msqrt><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>�</mi></msqrt></mrow><mi>tan</mi><mo></mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x={\sqrt {c/a}}\tan \theta }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1de09a0ac663753a96ae78717c425a08b4a15c96" style="border: 0px; display: inline-block; height: 4.843ex; margin: 0px; vertical-align: -1.838ex; width: 15.375ex;" /></span></p><p style="margin: 0.5em 0px 1em;">dan kemudian mengalikannya dengan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">cos<sup style="font-size: 13.216px; line-height: 1;">2</sup><i>θ</i></span>, kami dapatkan</p><p style="margin: 0.5em 0px 1em;"><b>[3]</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \sin ^{2}\theta +{\frac {b}{\sqrt {ac}}}\sin \theta \cos \theta \pm \cos ^{2}\theta =0.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>sin</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo></mo><mi>�</mi><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><msqrt><mi>�</mi><mi>�</mi></msqrt></mfrac></mrow><mi>sin</mi><mo></mo><mi>�</mi><mi>cos</mi><mo></mo><mi>�</mi><mo>±</mo><msup><mi>cos</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo></mo><mi>�</mi><mo>=</mo><mn>0.</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \sin ^{2}\theta +{\frac {b}{\sqrt {ac}}}\sin \theta \cos \theta \pm \cos ^{2}\theta =0.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/048669c49b51f2f4c00ec57d1e2ffaf292f5b102" style="border: 0px; display: inline-block; height: 6.343ex; margin: 0px; vertical-align: -2.838ex; width: 36.324ex;" /></span></p><p style="margin: 0.5em 0px 1em;">Memperkenalkan fungsi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">2<i>θ</i></span> dan mengatur ulang, kami dapatkan</p><p style="margin: 0.5em 0px 1em;"><b>[4]</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \tan 2\theta _{n}=+2{\frac {\sqrt {ac}}{b}},}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>tan</mi><mo></mo><mn>2</mn><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo>=</mo><mo>+</mo><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mfrac><msqrt><mi>�</mi><mi>�</mi></msqrt><mi>�</mi></mfrac></mrow><mo>,</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \tan 2\theta _{n}=+2{\frac {\sqrt {ac}}{b}},}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e5e680a38d29430ecd18b0b892658331b24951d" style="border: 0px; display: inline-block; height: 6.009ex; margin: 0px; vertical-align: -2.005ex; width: 18.943ex;" /></span></p><p style="margin: 0.5em 0px 1em;"><b>[5]</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \sin 2\theta _{p}=-2{\frac {\sqrt {ac}}{b}},}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>sin</mi><mo></mo><mn>2</mn><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo>=</mo><mo>−</mo><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mfrac><msqrt><mi>�</mi><mi>�</mi></msqrt><mi>�</mi></mfrac></mrow><mo>,</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \sin 2\theta _{p}=-2{\frac {\sqrt {ac}}{b}},}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/622221ccea1dffd8e39785e41137af8fd28c6be2" style="border: 0px; display: inline-block; height: 6.009ex; margin: 0px; vertical-align: -2.005ex; width: 18.279ex;" /></span></p><p style="margin: 0.5em 0px 1em;">Dimana tulisan di bawah garis <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>n</i></span> and <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>p</i></span> sesuai, masing-masing, dengan penggunaan tanda negatif atau positif dalam persamaan <b>[1]</b>. Mengganti nilai dua <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>θ</i><sub style="font-size: 13.216px; line-height: 1;">n</sub></span> atau <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>θ</i><sub style="font-size: 13.216px; line-height: 1;">p</sub></span> ditemukan dari persamaan <b>[4]</b> atau <b>[5]</b> menjadi <b>[2]</b> memberikan akar yang dibutuhkan <b>[1]</b>. Akar kompleks terjadi dalam solusi berdasarkan persamaan <b>[5]</b> bila nilai absolut <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">sin 2<i>θ</i><sub style="font-size: 13.216px; line-height: 1;">p</sub></span> melebihi persatuan. Jumlah upaya yang terlibat dalam menyelesaikan persamaan kuadrat menggunakan strategi pencarian tabel trigonometri dan logaritmik campuran ini adalah dua pertiga dari upaya menggunakan tabel logaritmik juga..<sup class="reference" id="cite_ref-Seares1945_2-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Persamaan_kuadrat#cite_note-Seares1945-2" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[2]</a></sup> Menghitung akar kompleks akan membutuhkan penggunaan bentuk trigonometri yang berbeda.<sup class="reference" id="cite_ref-Aude1938_3-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Persamaan_kuadrat#cite_note-Aude1938-3" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[3]</a></sup></p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;">Untuk mengilustrasikan, mari kita asumsikan bahwa kita memiliki tabel logaritma tujuh tempat dan tabel trigonometri yang tersedia, dan ingin menyelesaikan hal-hal berikut ini untuk akurasi enam angka penting:<dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 4.16130x^{2}+9.15933x-11.4207=0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>4.16130</mn><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mn>9.15933</mn><mi>�</mi><mo>−</mo><mn>11.4207</mn><mo>=</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 4.16130x^{2}+9.15933x-11.4207=0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ac5d57e3a9c2b043b5b20c96965afbace02f40c" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.505ex; width: 36.52ex;" /></span></dd></dl></dd></dl></dd></dl><ol style="list-style-image: none; margin: 0.3em 0px 0px 3.2em; padding: 0px;"><li style="margin-bottom: 0.1em;">Tabel pemeta tujuh tempat mungkin hanya memiliki 100.000 entri, dan menghitung hasil antara ke tujuh tempat umumnya akan memerlukan interpolasi antara entri yang berdekatan.</li><li style="margin-bottom: 0.1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \log a=0.6192290,\log b=0.9618637,\log c=1.0576927}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>log</mi><mo></mo><mi>�</mi><mo>=</mo><mn>0.6192290</mn><mo>,</mo><mi>log</mi><mo></mo><mi>�</mi><mo>=</mo><mn>0.9618637</mn><mo>,</mo><mi>log</mi><mo></mo><mi>�</mi><mo>=</mo><mn>1.0576927</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \log a=0.6192290,\log b=0.9618637,\log c=1.0576927}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/473b697123e82e5e57248ca9c34641677bc5f4d9" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 54.513ex;" /></span></li><li style="margin-bottom: 0.1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 2{\sqrt {ac}}/b=2\times 10^{(0.6192290+1.0576927)/2-0.9618637}=1.505314}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><msqrt><mi>�</mi><mi>�</mi></msqrt></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>�</mi><mo>=</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">(</mo><mn>0.6192290</mn><mo>+</mo><mn>1.0576927</mn><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn><mo>−</mo><mn>0.9618637</mn></mrow></msup><mo>=</mo><mn>1.505314</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 2{\sqrt {ac}}/b=2\times 10^{(0.6192290+1.0576927)/2-0.9618637}=1.505314}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40828471d32825ad8ce6d3279d6a5af942316546" style="border: 0px; display: inline-block; height: 3.509ex; vertical-align: -1.005ex; width: 55.616ex;" /></span></li><li style="margin-bottom: 0.1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \theta =(\tan ^{-1}1.505314)/2=28.20169^{\circ }{\text{ or }}-61.79831^{\circ }}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><mo stretchy="false">(</mo><msup><mi>tan</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><mo></mo><mn>1.505314</mn><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn><mo>=</mo><msup><mn>28.20169</mn><mrow class="MJX-TeXAtom-ORD"><mo>∘</mo></mrow></msup><mrow class="MJX-TeXAtom-ORD"><mtext> or </mtext></mrow><mo>−</mo><msup><mn>61.79831</mn><mrow class="MJX-TeXAtom-ORD"><mo>∘</mo></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \theta =(\tan ^{-1}1.505314)/2=28.20169^{\circ }{\text{ or }}-61.79831^{\circ }}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9171f460f0ecb2412357f3f6d946fa762fd9b86c" style="border: 0px; display: inline-block; height: 3.176ex; vertical-align: -0.838ex; width: 52.037ex;" /></span></li><li style="margin-bottom: 0.1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \log |\tan \theta |=-0.2706462{\text{ or }}0.2706462}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>log</mi><mo></mo><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mi>tan</mi><mo></mo><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mo>=</mo><mo>−</mo><mn>0.2706462</mn><mrow class="MJX-TeXAtom-ORD"><mtext> or </mtext></mrow><mn>0.2706462</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \log |\tan \theta |=-0.2706462{\text{ or }}0.2706462}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5331efc8361eb2d9f96c2d11d19f3f1f9b3d3412" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.838ex; width: 37.912ex;" /></span></li><li style="margin-bottom: 0.1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \log {\sqrt {c/a}}=(1.0576927-0.6192290)/2=0.2192318}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>log</mi><mo></mo><mrow class="MJX-TeXAtom-ORD"><msqrt><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>�</mi></msqrt></mrow><mo>=</mo><mo stretchy="false">(</mo><mn>1.0576927</mn><mo>−</mo><mn>0.6192290</mn><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn><mo>=</mo><mn>0.2192318</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \log {\sqrt {c/a}}=(1.0576927-0.6192290)/2=0.2192318}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c704c57664833acd6a6344f1292fa64d1fbe01c" style="border: 0px; display: inline-block; height: 4.843ex; vertical-align: -1.838ex; width: 52.093ex;" /></span></li><li style="margin-bottom: 0.1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1}=10^{0.2192318-0.2706462}=0.888353}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>=</mo><msup><mn>10</mn><mrow class="MJX-TeXAtom-ORD"><mn>0.2192318</mn><mo>−</mo><mn>0.2706462</mn></mrow></msup><mo>=</mo><mn>0.888353</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1}=10^{0.2192318-0.2706462}=0.888353}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/279da5203bdca2ac14b06f678bef5cfc70f3a61f" style="border: 0px; display: inline-block; height: 3.009ex; vertical-align: -0.671ex; width: 35.267ex;" /></span> (dibulatkan menjadi enam angka penting)</li></ol><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{2}=-10^{0.2192318+0.2706462}=-3.08943}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>=</mo><mo>−</mo><msup><mn>10</mn><mrow class="MJX-TeXAtom-ORD"><mn>0.2192318</mn><mo>+</mo><mn>0.2706462</mn></mrow></msup><mo>=</mo><mo>−</mo><mn>3.08943</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{2}=-10^{0.2192318+0.2706462}=-3.08943}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/320cf8b5e1fc09067fe5fff45987b6954b36c692" style="border: 0px; display: inline-block; height: 3.009ex; vertical-align: -0.671ex; width: 37.721ex;" /></span></dd></dl></dd></dl><h4 style="color: black; font-size: 14px; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Solusi_untuk_akar_kompleks_di_koordinat_polar">Solusi untuk akar kompleks di koordinat polar</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&veaction=edit&section=15" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Solusi untuk akar kompleks di koordinat polar">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&action=edit&section=15" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Solusi untuk akar kompleks di koordinat polar">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h4><p style="margin: 0.5em 0px 1em;">Jika persamaan kuadrat <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ax^{2}+bx+c=0}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>�</mi><mi>�</mi><mo>+</mo><mi>�</mi><mo>=</mo><mn>0</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ax^{2}+bx+c=0}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23e70cfa003f402d108ec04d97983fb62f69536e" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -0.505ex; width: 16.89ex;" /></span> dengan koefisien nyata memiliki dua akar kompleks dalam kasus di mana <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle b^{2}-4ac<0,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−</mo><mn>4</mn><mi>�</mi><mi>�</mi><mo><</mo><mn>0</mn><mo>,</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle b^{2}-4ac<0,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5a3f7136258dba30bee6fba1a286f77b5d4f4122" style="border: 0px; display: inline-block; height: 3.009ex; margin: 0px; vertical-align: -0.671ex; width: 13.199ex;" /></span> membutuhkan <i>a</i> dan <i>c</i> untuk memiliki tanda yang sama pada solusi untuk akar dapat diekspresikan dalam bentuk polar sebagai<sup class="reference" id="cite_ref-4" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Persamaan_kuadrat#cite_note-4" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[4]</a></sup></p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x_{1},\,x_{2}=r(\cos \theta \pm i\sin \theta ),}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>,</mo><mspace width="thinmathspace"></mspace><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo>=</mo><mi>�</mi><mo stretchy="false">(</mo><mi>cos</mi><mo></mo><mi>�</mi><mo>±</mo><mi>�</mi><mi>sin</mi><mo></mo><mi>�</mi><mo stretchy="false">)</mo><mo>,</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x_{1},\,x_{2}=r(\cos \theta \pm i\sin \theta ),}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c589d8db912f2800d95749dafaed6d61ce78c2b" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.838ex; width: 25.744ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">dimana <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle r={\sqrt {\tfrac {c}{a}}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><msqrt><mstyle displaystyle="false" scriptlevel="0"><mfrac><mi>�</mi><mi>�</mi></mfrac></mstyle></msqrt></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle r={\sqrt {\tfrac {c}{a}}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ab7f6afb0ea4ded6fa024cd12b04f8681170049" style="border: 0px; display: inline-block; height: 4.843ex; margin: 0px; vertical-align: -2.005ex; width: 8.177ex;" /></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \theta =\cos ^{-1}\left({\tfrac {-b}{2{\sqrt {ac}}}}\right).}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><msup><mi>cos</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><mo></mo><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mrow><mo>−</mo><mi>�</mi></mrow><mrow><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><msqrt><mi>�</mi><mi>�</mi></msqrt></mrow></mrow></mfrac></mstyle></mrow><mo>)</mo></mrow><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \theta =\cos ^{-1}\left({\tfrac {-b}{2{\sqrt {ac}}}}\right).}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72e4e5af6b512abf36eb32d2ba8bce704e339163" style="border: 0px; display: inline-block; height: 4.843ex; margin: 0px; vertical-align: -1.838ex; width: 17.664ex;" /></span></p><h4 style="color: black; font-size: 14px; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Solusi_geometris">Solusi geometris</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&veaction=edit&section=16" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Solusi geometris">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Persamaan_kuadrat&action=edit&section=16" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Solusi geometris">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h4><figure style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:LillsQuadratic.svg" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img alt="Gambar 6. Solusi geometris eh x kuadrat ditambah b x ditambah c = 0 menggunakan metode Lill. Konstruksi geometrisnya adalah sebagai berikut: Gambarlah sebuah trapesium S Eh B C. Garis S Eh dengan panjang eh adalah sisi kiri vertikal dari trapesium. Garis Eh B dengan panjang b adalah alas trapesium secara horizontal. Garis B C panjang c adalah sisi kanan vertikal trapesium. Garis C S melengkapi trapesium. Dari titik tengah garis C S, gambarlah sebuah lingkaran yang melewati titik C dan S. Tergantung pada panjang relatif dari eh, b, dan c, lingkaran tersebut bisa atau tidak memotong garis Eh B. Jika ya, maka persamaan tersebut memiliki solusi. Jika kita sebut titik potong X 1 dan X 2, maka kedua penyelesaian diberikan oleh negatif Eh X 1 dibagi S Eh, dan negatif Eh X 2 dibagi S Eh." class="mw-file-element" data-file-height="567" data-file-width="588" decoding="async" height="174" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d5/LillsQuadratic.svg/180px-LillsQuadratic.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/LillsQuadratic.svg/270px-LillsQuadratic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/LillsQuadratic.svg/360px-LillsQuadratic.svg.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="180" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Gambar 6. Solusi geometris <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>ax</i><sup style="font-size: 11.6829px; line-height: 1;">2</sup> + <i>bx</i> + <i>c</i> = 0</span> menggunakan metode Lill. Solusinya adalah −AX1/SA, −AX2/SA</figcaption></figure><p style="margin: 0.5em 0px 1em;">Persamaan kuadrat dapat diselesaikan secara geometris dengan beberapa cara. Salah satunya adalah melalui <a class="new" href="https://id.wikipedia.org/w/index.php?title=Metode_Lill&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Metode Lill (halaman belum tersedia)">metode Lill</a>. Tiga koefisien <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>a</i></span>, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i></span>, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>c</i></span> digambar dengan sudut siku-siku antara keduanya seperti pada SA, AB, dan BC pada Gambar 6. Sebuah lingkaran digambar dengan titik awal dan akhir SC sebagai diameter. Jika ini memotong garis tengah AB dari ketiganya maka persamaan tersebut memiliki solusi, dan solusi diberikan dengan jarak negatif sepanjang garis ini dari A dibagi dengan koefisien pertama <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>a</i></span> atau SA. Bila <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>a</i></span> ialah <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">1</span> koefisien dapat dibaca secara langsung. Jadi solusi dalam diagram adalah −AX1/SA dan −AX2/SA.<sup class="reference" id="cite_ref-5" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Persamaan_kuadrat#cite_note-5" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[5]</a></sup></p><figure class="mw-halign-left" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: left; display: table; float: left; line-height: 0; margin: 0.5em 1.4em 1.3em 0px; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:CarlyleCircle.svg" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img class="mw-file-element" data-file-height="104" data-file-width="150" decoding="async" height="208" src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e3/CarlyleCircle.svg/300px-CarlyleCircle.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/CarlyleCircle.svg/450px-CarlyleCircle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e3/CarlyleCircle.svg/600px-CarlyleCircle.svg.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="300" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Lingkaran Carlyle dari persamaan kuadrat <i>x</i><sup style="font-size: 9.9008px; line-height: 1;">2</sup> − <i>sx</i> + <i>p</i> = 0.</figcaption></figure><p style="margin: 0.5em 0px 1em;"><a class="new" href="https://id.wikipedia.org/w/index.php?title=Lingkaran_Carlyle&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Lingkaran Carlyle (halaman belum tersedia)">Lingkaran Carlyle</a>, dinamai <a href="https://id.wikipedia.org/wiki/Thomas_Carlyle" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Thomas Carlyle">Thomas Carlyle</a>, memiliki sifat bahwa solusi dari persamaan kuadrat adalah koordinat horizontal dari perpotongan lingkaran dengan <a class="mw-redirect mw-disambig" href="https://id.wikipedia.org/wiki/Horizontal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Horizontal">horizontal</a>.<sup class="reference" id="cite_ref-Wolfram_6-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Persamaan_kuadrat#cite_note-Wolfram-6" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[6]</a></sup> Lingkaran Carlyle telah digunakan untuk mengembangkan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Konstruksi_penggaris-dan-kompas&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Konstruksi penggaris-dan-kompas (halaman belum tersedia)">konstruksi penggaris-dan-kompas</a> dari <a class="new" href="https://id.wikipedia.org/w/index.php?title=Poligon_beraturan&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Poligon beraturan (halaman belum tersedia)">poligon beraturan</a>.</p><p style="margin: 0.5em 0px 1em;"><br /></p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); 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text-decoration-line: none;" title="Persamaan linier">Persamaan linier</a></li><li style="margin-bottom: 0.1em;"><a href="https://id.wikipedia.org/wiki/Fungsi_kubik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi kubik">Fungsi kubik</a></li><li style="margin-bottom: 0.1em;"><a href="https://id.wikipedia.org/wiki/Persamaan_kuartik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Persamaan kuartik">Persamaan kuartik</a></li><li style="margin-bottom: 0.1em;"><a class="mw-redirect" href="https://id.wikipedia.org/wiki/Persamaan_kuintik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Persamaan kuintik">Persamaan kuintik</a></li><li style="margin-bottom: 0.1em;"><a href="https://id.wikipedia.org/wiki/Teorema_dasar_aljabar" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teorema dasar aljabar">Teorema dasar aljabar</a></li></ul></div></div></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8185710560472973854.post-89286272721984337272024-01-29T13:44:00.001+07:002024-01-29T13:44:26.119+07:00Logaritma<p> </p><header class="mw-body-header vector-page-titlebar" style="align-items: center; 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margin-top: 8px;">Dari Wikipedia bahasa Indonesia, ensiklopedia bebas</div></div><div id="contentSub" style="color: #54595d; font-size: 0.875rem; margin: 8px 0px 0px; width: auto;"><div id="mw-content-subtitle"></div></div><div class="mw-body-content" id="mw-content-text" style="margin-top: 16px;"><div class="mw-content-ltr mw-parser-output" dir="ltr" lang="id"><figure style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Logarithm_plots.png" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img class="mw-file-element" data-file-height="1294" data-file-width="1706" decoding="async" height="228" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/81/Logarithm_plots.png/300px-Logarithm_plots.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Logarithm_plots.png/450px-Logarithm_plots.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/81/Logarithm_plots.png/600px-Logarithm_plots.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="300" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Grafik fungsi logaritma dengan tiga bilangan pokok yang umum. Titik khusus <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 11.6829px; line-height: 1;"><i>b</i></sup>log <i>b</i> = 1</span> diperlihatkan oleh garis bertitik, dan semua kurva fungsi memotong di <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 11.6829px; line-height: 1;"><i>b</i></sup>log 1 = 0</span>.</figcaption></figure><table class="sidebar nomobile" style="background: rgb(248, 249, 250); border-collapse: collapse; border: 1px solid rgb(170, 170, 170); clear: right; float: right; font-size: 12.32px; 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color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Penambahan">Penambahan</a> (+)</th></tr><tr><td style="text-align: right; vertical-align: middle;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 18.8989px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{suku}}\,+\,{\text{suku}}\\\scriptstyle {\text{yang ditambah}}\,+\,{\text{penambah}}\\\scriptstyle {\text{tinambah}}\,+\,{\text{penambah}}\end{matrix}}\right\}\,=\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="false" scriptlevel="1"><mrow><mo fence="true" stretchy="true" symmetric="true"></mo><mrow class="MJX-TeXAtom-ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>suku</mtext></mrow><mspace width="thinmathspace"></mspace><mo>+</mo><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mtext>suku</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>yang ditambah</mtext></mrow><mspace width="thinmathspace"></mspace><mo>+</mo><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mtext>penambah</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>tinambah</mtext></mrow><mspace width="thinmathspace"></mspace><mo>+</mo><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mtext>penambah</mtext></mrow></mstyle></mtd></mtr></mtable></mrow><mo>}</mo></mrow><mspace width="thinmathspace"></mspace><mo>=</mo><mspace width="thinmathspace"></mspace></mstyle></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{suku}}\,+\,{\text{suku}}\\\scriptstyle {\text{yang ditambah}}\,+\,{\text{penambah}}\\\scriptstyle {\text{tinambah}}\,+\,{\text{penambah}}\end{matrix}}\right\}\,=\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0abf25240789d26035c4b88fde8c1f7da5026a8f" style="border: 0px; 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display: inline-block; height: 4.843ex; margin-bottom: -0.303ex; vertical-align: -1.702ex; width: 19.942ex;" /></span></td><td style="vertical-align: middle;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 18.8989px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\begin{matrix}\scriptstyle {\text{selisih}}\\\scriptstyle {\text{beda}}\end{matrix}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>selisih</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>beda</mtext></mrow></mstyle></mtd></mtr></mtable></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\begin{matrix}\scriptstyle {\text{selisih}}\\\scriptstyle {\text{beda}}\end{matrix}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/741bcf4fe5f403567b1815645fc21616e0e64a2f" style="border: 0px; display: inline-block; height: 6.176ex; vertical-align: -2.505ex; width: 5.063ex;" /></span></td></tr><tr><th colspan="4" style="text-align: center; vertical-align: top;"><a href="https://id.wikipedia.org/wiki/Perkalian" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Perkalian">Perkalian</a> (×)</th></tr><tr><td style="text-align: right; vertical-align: middle;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 18.8989px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{faktor}}\,\times \,{\text{faktor}}\\\scriptstyle {\text{pengali}}\,\times \,{\text{kinali}}\end{matrix}}\right\}\,=\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="false" scriptlevel="1"><mrow><mo fence="true" stretchy="true" symmetric="true"></mo><mrow class="MJX-TeXAtom-ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>faktor</mtext></mrow><mspace width="thinmathspace"></mspace><mo>×</mo><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mtext>faktor</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>pengali</mtext></mrow><mspace width="thinmathspace"></mspace><mo>×</mo><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mtext>kinali</mtext></mrow></mstyle></mtd></mtr></mtable></mrow><mo>}</mo></mrow><mspace width="thinmathspace"></mspace><mo>=</mo><mspace width="thinmathspace"></mspace></mstyle></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{faktor}}\,\times \,{\text{faktor}}\\\scriptstyle {\text{pengali}}\,\times \,{\text{kinali}}\end{matrix}}\right\}\,=\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d81a91a53c7ed8e1aa9bde68515fa1585dbed6f8" style="border: 0px; display: inline-block; height: 4.843ex; margin-bottom: -0.303ex; vertical-align: -1.702ex; width: 15.182ex;" /></span></td><td style="vertical-align: middle;"><a href="https://id.wikipedia.org/wiki/Darab_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Darab (matematika)"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 18.8989px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\begin{matrix}\scriptstyle {\text{hasil kali}}\\\scriptstyle {\text{darab}}\end{matrix}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>hasil kali</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>darab</mtext></mrow></mstyle></mtd></mtr></mtable></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\begin{matrix}\scriptstyle {\text{hasil kali}}\\\scriptstyle {\text{darab}}\end{matrix}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c2fb9478ac37b88ea462b47d438cc854477404d" style="border: 0px; display: inline-block; height: 6.176ex; vertical-align: -2.505ex; width: 7.235ex;" /></a></td></tr><tr><th colspan="4" style="text-align: center; vertical-align: top;"><a href="https://id.wikipedia.org/wiki/Pembagian" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Pembagian">Pembagian</a> (÷), (/)</th></tr><tr><td style="text-align: right; vertical-align: middle;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 18.8989px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\frac {\scriptstyle {\text{dividen}}}{\scriptstyle {\text{pembagi}}}}\\\scriptstyle {\text{ }}\\\scriptstyle {\frac {\scriptstyle {\text{pembilang}}}{\scriptstyle {\text{penyebut}}}}\end{matrix}}\right\}\,=\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="false" scriptlevel="1"><mrow><mo fence="true" stretchy="true" symmetric="true"></mo><mrow class="MJX-TeXAtom-ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mfrac><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>dividen</mtext></mrow></mstyle><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>pembagi</mtext></mrow></mstyle></mfrac></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext> </mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mfrac><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>pembilang</mtext></mrow></mstyle><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>penyebut</mtext></mrow></mstyle></mfrac></mrow></mstyle></mtd></mtr></mtable></mrow><mo>}</mo></mrow><mspace width="thinmathspace"></mspace><mo>=</mo><mspace width="thinmathspace"></mspace></mstyle></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\frac {\scriptstyle {\text{dividen}}}{\scriptstyle {\text{pembagi}}}}\\\scriptstyle {\text{ }}\\\scriptstyle {\frac {\scriptstyle {\text{pembilang}}}{\scriptstyle {\text{penyebut}}}}\end{matrix}}\right\}\,=\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/190f9a94aeecc40c0cab70438dd9108c16b8c5d2" style="border: 0px; display: inline-block; height: 11.509ex; vertical-align: -5.338ex; width: 12.501ex;" /></span></td><td style="vertical-align: middle;"><a href="https://id.wikipedia.org/wiki/Hasil_bagi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Hasil bagi"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 18.8989px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\begin{matrix}\scriptstyle {\text{hasil bagi}}\\\scriptstyle {\text{pecahan}}\\\scriptstyle {\text{rasio}}\end{matrix}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>hasil bagi</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>pecahan</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>rasio</mtext></mrow></mstyle></mtd></mtr></mtable></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\begin{matrix}\scriptstyle {\text{hasil bagi}}\\\scriptstyle {\text{pecahan}}\\\scriptstyle {\text{rasio}}\end{matrix}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56c6ba77a51fc706430d79a566ab8eca3a462f80" style="border: 0px; display: inline-block; height: 9.176ex; vertical-align: -4.005ex; width: 7.646ex;" /></a></td></tr><tr><th colspan="4" style="text-align: center; vertical-align: top;"><a href="https://id.wikipedia.org/wiki/Eksponensiasi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Eksponensiasi">Eksponensiasi</a> (^)</th></tr><tr><td style="text-align: right; vertical-align: middle;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 18.8989px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \scriptstyle {\text{bilangan pokok}}^{\text{eksponen}}\,=\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="false" scriptlevel="1"><msup><mrow class="MJX-TeXAtom-ORD"><mtext>bilangan pokok</mtext></mrow><mrow class="MJX-TeXAtom-ORD"><mtext>eksponen</mtext></mrow></msup><mspace width="thinmathspace"></mspace><mo>=</mo><mspace width="thinmathspace"></mspace></mstyle></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \scriptstyle {\text{bilangan pokok}}^{\text{eksponen}}\,=\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68b8239a1c0b55a4929e7b376823a57c8189253e" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 18.523ex;" /></span></td><td style="vertical-align: middle;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 18.8989px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \scriptstyle {\text{pangkat}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>pangkat</mtext></mrow></mstyle></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \scriptstyle {\text{pangkat}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/116a830a8ccb0d8ad6fb450c3925836676bdcbd1" style="border: 0px; display: inline-block; height: 2.009ex; vertical-align: -0.671ex; width: 5.801ex;" /></span></td></tr><tr><th colspan="4" style="text-align: center; vertical-align: top;"><a href="https://id.wikipedia.org/wiki/Akar_bilangan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Akar bilangan">Penarikan akar</a> (√)</th></tr><tr><td style="text-align: right; vertical-align: middle;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 18.8989px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \scriptstyle {\sqrt[{\text{pangkat}}]{\scriptstyle {\text{radikan}}}}\,=\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mroot><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>radikan</mtext></mrow></mstyle><mrow class="MJX-TeXAtom-ORD"><mtext>pangkat</mtext></mrow></mroot></mrow><mspace width="thinmathspace"></mspace><mo>=</mo><mspace width="thinmathspace"></mspace></mstyle></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \scriptstyle {\sqrt[{\text{pangkat}}]{\scriptstyle {\text{radikan}}}}\,=\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b19418be0cf9ed355df169ae0dc3df1084139542" style="border: 0px; display: inline-block; height: 2.676ex; vertical-align: -0.505ex; width: 12.609ex;" /></span></td><td style="vertical-align: middle;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 18.8989px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \scriptstyle {\text{akar}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>akar</mtext></mrow></mstyle></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \scriptstyle {\text{akar}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d99ca490c5ebea5481bb86a79369e4b9f2c8c88" style="border: 0px; display: inline-block; height: 1.676ex; vertical-align: -0.338ex; width: 3.157ex;" /></span></td></tr><tr><th colspan="4" style="text-align: center; vertical-align: top;"><a class="mw-selflink selflink" style="background: none; color: inherit; cursor: pointer; overflow-wrap: break-word; text-decoration: inherit;">Logaritma</a> (log)</th></tr><tr><td style="text-align: right; vertical-align: middle;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 18.8989px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \scriptstyle ^{\text{bilangan pokok}}\!\log({\text{antilogaritma}})\,=\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="false" scriptlevel="1"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mtext>bilangan pokok</mtext></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mtext>antilogaritma</mtext></mrow><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace><mo>=</mo><mspace width="thinmathspace"></mspace></mstyle></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \scriptstyle ^{\text{bilangan pokok}}\!\log({\text{antilogaritma}})\,=\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b1bfc346c1502b92d3f49715adc05ad70f370a3" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 24.324ex;" /></span></td><td style="vertical-align: middle;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 18.8989px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \scriptstyle {\text{logaritma}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mtext>logaritma</mtext></mrow></mstyle></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \scriptstyle {\text{logaritma}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5984abf04597d718b2ce3cc99ef9fe3a4f9340f7" style="border: 0px; display: inline-block; height: 2.009ex; vertical-align: -0.671ex; width: 6.856ex;" /></span></td></tr></tbody></table></td></tr></tbody></table><p style="margin: 0.5em 0px 1em;">Dalam <a href="https://id.wikipedia.org/wiki/Matematika" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Matematika">matematika</a>, <b>logaritma</b> adalah <a href="https://id.wikipedia.org/wiki/Fungsi_invers" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi invers">fungsi invers</a> dari <a href="https://id.wikipedia.org/wiki/Eksponensiasi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Eksponensiasi">eksponensiasi</a>. Dengan kata lain, logaritma dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> adalah <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Eksponen" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Eksponen">eksponen</a> dengan <a href="https://id.wikipedia.org/wiki/Bilangan_pokok" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan pokok">bilangan pokok</a> <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> yang dipangkatkan dengan bilangan konstan lain agar memperoleh nilai <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>. Kasus sederhana dalam logaritma adalah menghitung jumlah munculnya faktor yang sama dalam perkalian berulang. Sebagai contoh, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">1000 = 10 × 10 × 10 = 10<sup style="font-size: 13.216px; line-height: 1;">3</sup></span> dibaca, "logaritma 1000 dengan bilangan pokok 10 sama dengan 3" atau dinotasikan sebagai <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;">10</sup>log (1000) = 3</span>. Logaritma dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> dengan <i>bilangan pokok</i> <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> dilambangkan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log <i>x</i></span>. Terkadang logaritma dilambangkan sebagai <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log<sub style="font-size: 13.216px; line-height: 1;"><i>b</i></sub> (<i>x</i>)</span> atau tanpa menggunakan tanda kurung, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log<sub style="font-size: 13.216px; line-height: 1;"><i>b</i></sub> <i>x</i></span>, atau bahkan tanpa menggunakan bilangan pokok khusus, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log <i>x</i></span>.</p><p style="margin: 0.5em 0px 1em;">Ada tiga bilangan pokok logaritma yang umum beserta kegunaannya. Logaritma dengan bilangan pokok <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">10</span> (<span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i> = 10</span>) disebut sebagai <a href="https://id.wikipedia.org/wiki/Logaritma_umum" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma umum">logaritma umum</a>, yang biasanya dipakai dalam ilmu sains dan rekayasa. Logaritma dengan dengan bilangan pokok <a href="https://id.wikipedia.org/wiki/E_(konstanta_matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="E (konstanta matematika)">bilangan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>e</i></span></a> (<span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i> ≈ 2.718</span>) disebut sebagai <a href="https://id.wikipedia.org/wiki/Logaritma_alami" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma alami">logaritma alami</a>, yang dipakai dengan luas dalam matematika dan fisika, karena dapat mempermudah perhitungan <a href="https://id.wikipedia.org/wiki/Integral" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Integral">integral</a> dan <a href="https://id.wikipedia.org/wiki/Turunan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan">turunan</a>. Logaritma dengan bilangan pokok <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">2</span> (<span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i> = 2</span>) disebut sebagai <a href="https://id.wikipedia.org/wiki/Logaritma_biner" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma biner">logaritma biner</a>, yang seringkali dipakai dalam <a href="https://id.wikipedia.org/wiki/Ilmu_komputer" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Ilmu komputer">ilmu komputer</a>.</p><p style="margin: 0.5em 0px 1em;">Logaritma diperkenalkan oleh <a href="https://id.wikipedia.org/wiki/John_Napier" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="John Napier">John Napier</a> pada tahun 1614 sebagai alat yang menyederhanakan perhitungan.<sup class="reference" id="cite_ref-1" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-1" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[1]</a></sup> Logaritma dipakai lebih cepat dalam navigator, ilmu sains, rekayasa, ilmu ukur wilayah, dan bidang lainnya untuk lebih mempermudah perhitungan nilai yang sangat akurat. Dengan menggunakan <a href="https://id.wikipedia.org/wiki/Tabel_matematika" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Tabel matematika">tabel logaritma</a>, cara yang membosankan seperti mengalikan digit yang banyak dapat digantikan dengan melihat tabel dan penjumlahan yang lebih mudah. Ini dapat dilakukan karena logaritma dari <a href="https://id.wikipedia.org/wiki/Darab_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Darab (matematika)">hasil kali</a> bilangan merupakan logaritma dari <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Penjumlahan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Penjumlahan">jumlah</a> faktor bilangan:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ^{b}\!\log(xy)=\,^{b}\!\log x+\,^{b}\!\log y,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mo>+</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mo>,</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ^{b}\!\log(xy)=\,^{b}\!\log x+\,^{b}\!\log y,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fadaf31996c98e92decc9ddbfcbc621398935ead" style="border: 0px; display: inline-block; height: 3.176ex; vertical-align: -0.838ex; width: 26.642ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">asalkan bahwa <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span>, <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> dan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> bilangan positif dan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i> ≠ 1</span>. <a href="https://id.wikipedia.org/wiki/Mistar_hitung" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Mistar hitung">Mistar hitung</a> yang juga berasal dari logaritma dapat mempermudah perhitungan tanpa menggunakan tabel, namun perhitungannya kurang akurat. <a href="https://id.wikipedia.org/wiki/Leonhard_Euler" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Leonhard Euler">Leonhard Euler</a> mengaitkan gagasan logaritma saat ini dengan <a href="https://id.wikipedia.org/wiki/Fungsi_eksponensial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi eksponensial">fungsi eksponensial</a> pada abad ke-18, dan juga memperkenalkan huruf <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">e</span> sebagai bilangan pokok dari logaritma alami.<sup class="reference" id="cite_ref-2" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-2" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[2]</a></sup></p><p style="margin: 0.5em 0px 1em;">Penerapan <a href="https://id.wikipedia.org/wiki/Skala_logaritmik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Skala logaritmik">skala logaritmik</a> dipakai dalam mengurangi kuantitas yang sangat besar menjadi lebih kecil. Sebagai contoh, <a href="https://id.wikipedia.org/wiki/Desibel" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Desibel">desibel</a> (dB) adalah <a href="https://id.wikipedia.org/wiki/Satuan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Satuan">satuan</a> yang digunakan untuk menyatakan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Tingkat_(kuantitas_logaritmik)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Tingkat (kuantitas logaritmik) (halaman belum tersedia)">rasio sebagai logaritma</a>, sebagian besar untuk kekuatan sinyal dan amplitudo (contoh umumnya pada <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Tekanan_suara" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Tekanan suara">tekanan suara</a>). Dalam kimia, <a href="https://id.wikipedia.org/wiki/PH" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="PH">pH</a> mengukur <a href="https://id.wikipedia.org/wiki/Asam" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Asam">keasaman</a> dari <a href="https://id.wikipedia.org/wiki/Larutan_berair" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Larutan berair">larutan berair</a> melalui logaritma. Logaritma umumnya dipakai dalam <a href="https://id.wikipedia.org/wiki/Rumus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Rumus">rumus</a> ilmiah, dalam pengukuran <a class="new" href="https://id.wikipedia.org/w/index.php?title=Teori_kompleksitas_komputasi&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Teori kompleksitas komputasi (halaman belum tersedia)">kompleksitas algoritma</a> dan objek geometris yang disebut sebagai <a href="https://id.wikipedia.org/wiki/Fraktal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fraktal">fraktal</a>. Logaritma juga membantu untuk menjelaskan <a href="https://id.wikipedia.org/wiki/Frekuensi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Frekuensi">frekuensi</a> rasio <a href="https://id.wikipedia.org/wiki/Interval_(musik)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Interval (musik)">interval musik</a>, ditemukan di rumus yang menghitung <a href="https://id.wikipedia.org/wiki/Bilangan_prima" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan prima">bilangan prima</a> atau <a class="new" href="https://id.wikipedia.org/w/index.php?title=Hampiran_Stirling&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Hampiran Stirling (halaman belum tersedia)">hampiran</a> <a href="https://id.wikipedia.org/wiki/Faktorial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Faktorial">faktorial</a>, memberikan gambaran dalam <a href="https://id.wikipedia.org/wiki/Psikofisika" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Psikofisika">psikofisika</a>, dan dapat membantu perhitungan <a href="https://id.wikipedia.org/wiki/Akuntansi_forensik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Akuntansi forensik">akuntansi forensik</a>.</p><p style="margin: 0.5em 0px 1em;">Konsep logaritma sebagai invers dari eksponensiasi juga memperluas ke struktur matematika lain. Namun pada umumnya, logaritma cenderung merupakan fungsi bernilai banyak. Sebagai contoh, <a class="new" href="https://id.wikipedia.org/w/index.php?title=Logaritma_kompleks&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma kompleks (halaman belum tersedia)">logaritma kompleks</a> merupakan <a href="https://id.wikipedia.org/wiki/Fungsi_invers" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi invers">invers</a> dari fungsi eksponensial pada <a href="https://id.wikipedia.org/wiki/Bilangan_kompleks" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan kompleks">bilangan kompleks</a>. Mirip dengan contoh sebelumnya, <a href="https://id.wikipedia.org/wiki/Logaritma_diskret" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma diskret">logaritma diskret</a> dalam grup hingga, merupakan invers fungsi eksponensial bernilai banyak yang memiliki kegunaan dalam <a href="https://id.wikipedia.org/wiki/Kriptografi_kunci_publik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kriptografi kunci publik">kriptografi kunci publik</a>.</p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Alasan">Alasan</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=1" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Alasan">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=1" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Alasan">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><figure class="mw-default-size mw-halign-right" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Binary_logarithm_plot_with_grid.png" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img alt="Grafik memperlihatkan kurva logaritmik yang memotong\ sumbu-x di dan mendekati negatif takhingga di sepanjang garis sumbu-y." class="mw-file-element" data-file-height="1292" data-file-width="1704" decoding="async" height="227" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Binary_logarithm_plot_with_grid.png/300px-Binary_logarithm_plot_with_grid.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Binary_logarithm_plot_with_grid.png/450px-Binary_logarithm_plot_with_grid.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Binary_logarithm_plot_with_grid.png/600px-Binary_logarithm_plot_with_grid.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="300" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Gambar memperlihatkan <a href="https://id.wikipedia.org/wiki/Grafik_fungsi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Grafik fungsi">grafik</a> logaritma dengan bilangan pokok 2 memotong <a href="https://id.wikipedia.org/wiki/Sistem_koordinat_Cartesius" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Sistem koordinat Cartesius">sumbu-<i>x</i></a> di <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>x</i> = 1</span> dan melalui titik <span class="nowrap" style="text-wrap: nowrap;">(2, 1)</span>, <span class="nowrap" style="text-wrap: nowrap;">(4, 2)</span>, dan <span class="nowrap" style="text-wrap: nowrap;">(8, 3)</span>, sebagai contoh, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log<sub style="font-size: 11.6829px; line-height: 1;">2</sub>(8) = 3</span> dan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">2<sup style="font-size: 11.6829px; line-height: 1;">3</sup> = 8</span>. Grafik tersebut dengan sembarang mendekati sumbu-<span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span>, namun <a href="https://id.wikipedia.org/wiki/Asimtot" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Asimtot">tidak mendekati sumbu-<i>x</i></a>.</figcaption></figure><p style="margin: 0.5em 0px 1em;">Operasi aritmetika yang paling dasar adalah <a href="https://id.wikipedia.org/wiki/Penambahan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Penambahan">penambahan</a>, <a href="https://id.wikipedia.org/wiki/Perkalian" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Perkalian">perkalian</a>, dan <a href="https://id.wikipedia.org/wiki/Eksponensiasi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Eksponensiasi">eksponen</a>. Kebalikan dari penambahan adalah <a href="https://id.wikipedia.org/wiki/Pengurangan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Pengurangan">pengurangan</a>, dan kebalikan dari perkalian adalah <a href="https://id.wikipedia.org/wiki/Pembagian" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Pembagian">pembagian</a>. Mirip dengan contoh sebelumnya, logaritma merupakan kebalikan (atau invers) dari operasi <a href="https://id.wikipedia.org/wiki/Eksponensiasi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Eksponensiasi">eksponensiasi</a>. Eksponensiasi adalah bilangan <i>bilangan pokok</i> <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> yang ketika dipangkatkan dengan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> memberikan nilai <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>. Ini dirumuskan sebagai</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle b^{y}=x.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>=</mo><mi>�</mi><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle b^{y}=x.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32d862a261be92079096455ce1af882eb1c15f99" style="border: 0px; display: inline-block; height: 2.343ex; vertical-align: -0.338ex; width: 7.122ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Sebagai contoh, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">2</span> pangkat <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">3</span> memberikan nilai <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">8</span>. Secara matematis, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 2^{3}=8}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup><mo>=</mo><mn>8</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 2^{3}=8}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb2dded8eba905e4a019b70abad935422b198db4" style="border: 0px; display: inline-block; height: 2.676ex; margin: 0px; vertical-align: -0.338ex; width: 6.478ex;" /></span>.</p><p style="margin: 0.5em 0px 1em;">Logaritma dengan bilangan pokok <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> adalah operasi invers yang menyediakan nilai keluaran <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> dari nilai masukan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>. Hal ini mengartikan bahwa <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>y</i> = <sup style="font-size: 13.216px; line-height: 1;">b</sup>log <i>x</i></span> ekuivalen dengan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>x</i> = <i>b</i><sup style="font-size: 13.216px; line-height: 1;"><i>y</i></sup></span>, jika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Bilangan_real" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan real">bilangan real</a> positif. (Jika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> bukanlah bilangan real positif, eksponensiasi dan logaritma dapat terdefinisi tetapi membutuhkan beberapa nilai, sehingga definisi darinya semakin rumit.)</p><p style="margin: 0.5em 0px 1em;">Salah satu alasan bersejarah utamanya dalam memperkenalkan logaritma adalah rumus</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ^{b}\!\log(xy)=\,^{b}\!\log x+\,^{b}\!\log y,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mo>+</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mo>,</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ^{b}\!\log(xy)=\,^{b}\!\log x+\,^{b}\!\log y,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fadaf31996c98e92decc9ddbfcbc621398935ead" style="border: 0px; display: inline-block; height: 3.176ex; vertical-align: -0.838ex; width: 26.642ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">yang dapat mempermudah perhitungan nilai perkalian dan pembagian dengan penjumlahan, pengurangan, dan melihat <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Tabel_logaritma" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Tabel logaritma">tabel logaritma</a>. Perhitungan ini dipakai sebelum komputer ditemukan.</p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Definisi">Definisi</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=2" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Definisi">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=2" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Definisi">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><p style="margin: 0.5em 0px 1em;">Diberikan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Bilangan_real" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan real">bilangan real</a> positif <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> sehingga <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i> ≠ 1</span>, maka <i>logaritma</i> dari bilangan real positif <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> terhadap bilangan pokok <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span><sup class="reference" id="cite_ref-3" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-3" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[nb 1]</a></sup> adalah eksponen dengan bilangan pokok <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> yang dipangkatkan bilangan agar memperoleh nilai <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>. Dengan kata lain, logaritma bilangan pokok <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> adalah bilangan real <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> sehingga <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i><sup style="font-size: 13.216px; line-height: 1;"><i>y</i></sup> = <i>x</i></span>.<sup class="reference" id="cite_ref-4" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-4" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[3]</a></sup> Logaritma dilambangkan sebagai <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log <i>x</i></span> (dibaca "logaritma <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> dengan bilangan pokok <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span>"). Terdapat definisi yang mirip dan lebih ringkas mengatakan bahwa fungsi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log</span> <a href="https://id.wikipedia.org/wiki/Fungsi_invers" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi invers">invers</a> dengan fungsi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>x</i> ↦ <i>b</i><sup style="font-size: 13.216px; line-height: 1;"><i>x</i></sup></span>.</p><p style="margin: 0.5em 0px 1em;">Sebagai contoh, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;">2</sup>log 16 = 4</span>, karena <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">2<sup style="font-size: 13.216px; line-height: 1;">4</sup> = 2 × 2 × 2 × 2 = 16</span>. Logaritma juga dapat bernilai negatif, contohnya <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;">2</sup>log <span class="sfrac nowrap" style="display: inline-block; font-size: 14.042px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;">1</span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;">2</span></span> = –1</span>, karena <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">2<sup style="font-size: 13.216px; line-height: 1;">–1</sup> = <span class="sfrac nowrap" style="display: inline-block; font-size: 14.042px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;">1</span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;">2<sup style="font-size: 11.2336px; line-height: 1;">1</sup></span></span> = <span class="sfrac nowrap" style="display: inline-block; font-size: 14.042px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;">1</span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;">2</span></span></span>. Logaritma juga berupa nilai desimal, sebagai contoh <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;">10</sup>log 150</span> kira-kira sama dengan 2,176 karena terletak di antara 2 dan 3, dan begitupula 150 terletak antara <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">10<sup style="font-size: 13.216px; line-height: 1;">2</sup> = 100</span> dan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">10<sup style="font-size: 13.216px; line-height: 1;">3</sup> = 1000</span>. Adapun sifat logaritma bahwa untuk setiap <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span>, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log <i>b</i> = 1</span> karena <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i><sup style="font-size: 13.216px; line-height: 1;">1</sup> = <span class="texhtml mvar" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">b</span></span>, dan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log 1 = 0</span> karena <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i><sup style="font-size: 13.216px; line-height: 1;">0</sup> = 1</span>.</p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Identitas_logaritma">Identitas logaritma</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=3" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Identitas logaritma">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=3" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Identitas logaritma">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><div class="hatnote navigation-not-searchable" role="note" style="font-style: italic; margin-bottom: 0.5em; padding-left: 1.6em;">Artikel utama: <a href="https://id.wikipedia.org/wiki/Daftar_identitas_logaritma" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Daftar identitas logaritma">Daftar identitas logaritma</a></div><p style="margin: 0.5em 0px 1em;">Ada beberapa rumus penting yang mengaitkan logaritma dengan yang lainnya.<sup class="reference" id="cite_ref-5" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-5" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[4]</a></sup></p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span id="Hasil_kali.2C_hasil_bagi.2C_pangkat.2C_dan_akar"></span><span class="mw-headline" id="Hasil_kali,_hasil_bagi,_pangkat,_dan_akar">Hasil kali, hasil bagi, pangkat, dan akar</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=4" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Hasil kali, hasil bagi, pangkat, dan akar">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=4" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Hasil kali, hasil bagi, pangkat, dan akar">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;">Logaritma dari hasil kali merupakan jumlah logaritma dari bilangan yang dikalikan, dan logaritma dari hasil bagi dari dua bilangan merupakan selisih logaritma. Logaritma dari bilangan pangkat ke-<span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">p</span> sama dengan <i><span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">p</span></i> dikali logaritma dari bilangan tersendiri, dan logaritma bilangan akar ke-<span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">p</span> sama dengan logaritma dibagi dengan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">p</span>. Tabel berikut memuat daftar sifat-sifat logaritma tersebut beserta contohnya. Masing-masing identitas ini diperoleh dari hasil substitusi dari definisi logaritma <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x=b^{\,^{b}\!\log x}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x=b^{\,^{b}\!\log x}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7d6be1df7afc4f6a0d28fccb70b40140a742a4a" style="border: 0px; display: inline-block; height: 3.009ex; margin: 0px; vertical-align: -0.338ex; width: 10.211ex;" /></span> atau <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y=b^{\,^{b}\!\log y}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y=b^{\,^{b}\!\log y}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fcf3028d4d2c0e72f4a2e3d978e0618f19166125" style="border: 0px; display: inline-block; height: 3.343ex; margin: 0px; vertical-align: -0.671ex; width: 9.913ex;" /></span> pada ruas kiri persamaan.</p><table class="wikitable" style="background-color: #f8f9fa; border-collapse: collapse; border: 1px solid rgb(162, 169, 177); color: #202122; font-size: 14px; margin: 0px auto;"><tbody><tr><th style="background-color: #eaecf0; border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em; text-align: center;"></th><th style="background-color: #eaecf0; border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em; text-align: center;">Rumus</th><th style="background-color: #eaecf0; border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em; text-align: center;">Contoh</th></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;">Hasil kali</td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\textstyle ^{b}\!\log(xy)=\,^{b}\!\log x+\,^{b}\!\log y}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mo>+</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\textstyle ^{b}\!\log(xy)=\,^{b}\!\log x+\,^{b}\!\log y}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42b7a55ec5ce9cbfad34349aff676b26f6bd0489" style="border: 0px; display: inline-block; height: 3.009ex; vertical-align: -0.838ex; width: 25.995ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\textstyle ^{3}\!\log 243=\,^{3}\!\log(9\cdot 27)=^{3}\!\log 9+\,^{3}\!\log 27=2+3=5}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>243</mn><mo>=</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mo stretchy="false">(</mo><mn>9</mn><mo>⋅</mo><mn>27</mn><mo stretchy="false">)</mo><msup><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>9</mn><mo>+</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>27</mn><mo>=</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>=</mo><mn>5</mn></mstyle></mrow></semantics></math></span><img alt="{\textstyle ^{3}\!\log 243=\,^{3}\!\log(9\cdot 27)=^{3}\!\log 9+\,^{3}\!\log 27=2+3=5}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f56a1fa0759fd83b711f4f453ed06d0cd771e2c7" style="border: 0px; display: inline-block; height: 3.009ex; vertical-align: -0.838ex; width: 53.165ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;">Hasil bagi</td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\textstyle ^{b}\!\log \!{\frac {x}{y}}=\,^{b}\!\log x-\,^{b}\!\log y}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mspace width="negativethinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mo>=</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mo>−</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\textstyle ^{b}\!\log \!{\frac {x}{y}}=\,^{b}\!\log x-\,^{b}\!\log y}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bdbf21fb73f27cca111953fa92b75d0ed903dcb7" style="border: 0px; display: inline-block; height: 3.509ex; vertical-align: -1.338ex; width: 23.477ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\textstyle ^{2}\!\log 16=\,^{2}\!\log \!{\frac {64}{4}}=\,^{2}\!\log 64-\,^{2}\!\log 4=6-2=4}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>16</mn><mo>=</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mspace width="negativethinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>64</mn><mn>4</mn></mfrac></mrow><mo>=</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>64</mn><mo>−</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>4</mn><mo>=</mo><mn>6</mn><mo>−</mo><mn>2</mn><mo>=</mo><mn>4</mn></mstyle></mrow></semantics></math></span><img alt="{\textstyle ^{2}\!\log 16=\,^{2}\!\log \!{\frac {64}{4}}=\,^{2}\!\log 64-\,^{2}\!\log 4=6-2=4}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18134f21e507c0acb7ff817c6a616029588aeef8" style="border: 0px; display: inline-block; height: 3.676ex; vertical-align: -1.171ex; width: 48.281ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;">Pangkat</td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\textstyle ^{b}\!\log \left(x^{p}\right)=p\,^{b}\!\log x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mrow><mo>(</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>)</mo></mrow><mo>=</mo><mi>�</mi><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\textstyle ^{b}\!\log \left(x^{p}\right)=p\,^{b}\!\log x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ca4784feb1206b1ea865e2670c863c4763eed7e" style="border: 0px; display: inline-block; height: 3.009ex; vertical-align: -0.838ex; width: 18.389ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\textstyle ^{2}\!\log 64=\,^{2}\!\log \left(2^{6}\right)=6\cdot \,^{2}\!\log 2=6}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>64</mn><mo>=</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mrow><mo>(</mo><msup><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mn>6</mn></mrow></msup><mo>)</mo></mrow><mo>=</mo><mn>6</mn><mo>⋅</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>2</mn><mo>=</mo><mn>6</mn></mstyle></mrow></semantics></math></span><img alt="{\textstyle ^{2}\!\log 64=\,^{2}\!\log \left(2^{6}\right)=6\cdot \,^{2}\!\log 2=6}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac1c0116aebc87248b057a48ed1b601c2fa42371" style="border: 0px; display: inline-block; height: 3.343ex; vertical-align: -1.005ex; width: 34.76ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;">Akar</td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\textstyle ^{b}\!\log {\sqrt[{p}]{x}}={\frac {^{b}\!\log x}{p}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mrow class="MJX-TeXAtom-ORD"><mroot><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></mroot></mrow><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mrow><mi>�</mi></mfrac></mrow></mstyle></mrow></semantics></math></span><img alt="{\textstyle ^{b}\!\log {\sqrt[{p}]{x}}={\frac {^{b}\!\log x}{p}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0c1e18a9c48fb08b3dbbf2387e0646fefcc3303" style="border: 0px; display: inline-block; height: 4.509ex; vertical-align: -1.338ex; width: 15.662ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\textstyle ^{10}\!\log {\sqrt {1000}}=\,{\frac {1}{2}}\cdot \,^{10}\!\log 1000={\frac {3}{2}}=1,5}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mrow class="MJX-TeXAtom-ORD"><msqrt><mn>1000</mn></msqrt></mrow><mo>=</mo><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>⋅</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>1000</mn><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow><mo>=</mo><mn>1</mn><mo>,</mo><mn>5</mn></mstyle></mrow></semantics></math></span><img alt="{\textstyle ^{10}\!\log {\sqrt {1000}}=\,{\frac {1}{2}}\cdot \,^{10}\!\log 1000={\frac {3}{2}}=1,5}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/94afce6ef6929e33bee619e0040b02d3684208fb" style="border: 0px; display: inline-block; height: 3.509ex; vertical-align: -1.171ex; width: 40.129ex;" /></span></td></tr></tbody></table><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Mengubah_bilangan_pokok">Mengubah bilangan pokok</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=5" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Mengubah bilangan pokok">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=5" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Mengubah bilangan pokok">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;">Logaritma <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log <i>x</i></span> dapat dihitung sebagai hasil bagi logaritma <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> dengan logaritma <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> terhadap bilangan pokok sembarang <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">k</span>. Secara matematis dirumuskan sebagai:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ^{b}\!\log x={\frac {^{k}\!\log x}{^{k}\!\log b}}.\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mrow><mrow><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mrow></mfrac></mrow><mo>.</mo><mspace width="thinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ^{b}\!\log x={\frac {^{k}\!\log x}{^{k}\!\log b}}.\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/897d480dbb249738f56be9a2e86d270b06ea5df0" style="border: 0px; display: inline-block; height: 6.676ex; vertical-align: -2.671ex; width: 16.372ex;" /></span></dd></dl><div style="margin-left: 0px;"><table class="mw-collapsible mw-collapsed mw-made-collapsible" style="background: transparent; border: 1px solid silver; clear: both; font-size: 14px; margin: 0.2em auto auto; padding: 1px; width: 758.391px;"><tbody><tr><th style="background: rgb(240, 242, 245); font-size: 12.18px; padding: 0.2em 0.3em; text-align: center;"><button aria-expanded="false" class="mw-collapsible-toggle mw-collapsible-toggle-default mw-collapsible-toggle-collapsed" style="appearance: none; background-attachment: initial; background-clip: initial; background-image: none; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border-color: initial; border-style: initial; border-width: 0px; cursor: pointer; float: right; font-family: inherit; font-feature-settings: inherit; font-kerning: inherit; font-optical-sizing: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-variation-settings: inherit; font-weight: normal; line-height: inherit; margin: 0px; padding: 0px 0.2em; text-align: right; user-select: none;" tabindex="0" type="button"><span class="mw-collapsible-text" style="color: #3366cc;">tampil</span></button><span style="font-size: 14.007px;">Bukti konversi antara logaritma dari bilangan pokok sembarang</span></th></tr></tbody></table></div><p style="margin: 0.5em 0px 1em;"><a href="https://id.wikipedia.org/wiki/Kalkulator_ilmiah" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kalkulator ilmiah">Kalkulator ilmiah</a> merupakan alat yang menghitung logaritma dengan bilangan pokok 10 dan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><a href="https://id.wikipedia.org/wiki/E_(konstanta_matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="E (konstanta matematika)">e</a></span>.<sup class="reference" id="cite_ref-6" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-6" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[5]</a></sup> Logaritma terhadap setiap bilangan pokok <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> dapat ditentukan menggunakan kedua logaritma tersebut melalui rumus sebelumnya:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ^{b}\!\log x={\frac {^{10}\!\log x}{^{10}\!\log b}}={\frac {^{e}\!\log x}{^{e}\!\log b}}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mrow><mrow><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mrow></mfrac></mrow><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mrow><mrow><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mrow></mfrac></mrow><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ^{b}\!\log x={\frac {^{10}\!\log x}{^{10}\!\log b}}={\frac {^{e}\!\log x}{^{e}\!\log b}}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aaf9bcdbff50986732c47e623bae318c91597a33" style="border: 0px; display: inline-block; height: 6.343ex; vertical-align: -2.505ex; width: 26.394ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Diberikan suatu bilangan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> dan logaritma <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>y</i> = <sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log <i>x</i></span>, dengan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> adalah bilangan pokok yang tidak diketahui. Bilangan pokok tersebut dapat dinyatakan dengan</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle b=x^{\frac {1}{y}},}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mi>�</mi></mfrac></mrow></msup><mo>,</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle b=x^{\frac {1}{y}},}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3fd9660ce8c1b5ba4ef5d2f1f08a8ed5dde5a08" style="border: 0px; display: inline-block; height: 3.843ex; vertical-align: -0.671ex; width: 7.808ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Rumus ini dapat diperlihatkan dengan mengambil persamaan yang mendefinisikan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>x</i> = <i>b</i><sup style="font-size: 13.216px; line-height: 1;"><sup style="font-size: 10.5728px; line-height: 1;"><i>b</i></sup>log <i>x</i></sup> = <i>b</i><sup style="font-size: 13.216px; line-height: 1;"><i>y</i></sup></span>, lalu dipangkatkan dengan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><span class="sfrac nowrap" style="display: inline-block; font-size: 14.042px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;">1</span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;">y</span></span></span>.</p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Bilangan_pokok_khusus">Bilangan pokok khusus</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=6" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Bilangan pokok khusus">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=6" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Bilangan pokok khusus">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><figure class="mw-default-size" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Log4.svg" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img class="mw-file-element" data-file-height="500" data-file-width="575" decoding="async" height="191" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Log4.svg/220px-Log4.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Log4.svg/330px-Log4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Log4.svg/440px-Log4.svg.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="220" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Grafik logaritma dengan bilangan pokok 0,5; 2; dan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">e</span></figcaption></figure><p style="margin: 0.5em 0px 1em;">Secara khusus, terdapat tiga bilangan pokok yang umum di antara semua pilihan bilangan pokok pada logaritma. Ketiga bilangan pokok tersebut adalah <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i> = 10</span>, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i> = <a href="https://id.wikipedia.org/wiki/E_(konstanta_matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="E (konstanta matematika)"><i>e</i></a></span> (konstanta <a href="https://id.wikipedia.org/wiki/Bilangan_irasional" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan irasional">bilangan irasional</a> yang kira-kira sama dengan 2,71828), dan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i> = 2</span> (<a href="https://id.wikipedia.org/wiki/Logaritma_biner" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma biner">logaritma biner</a>). Dalam <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Analisis_matematika" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Analisis matematika">analisis matematika</a>, logaritma dengan bilangan pokok <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">e</span> tersebar karena sifat analitik yang dijelaskan di bawah. Di sisi lain, logaritma dengan <span class="nowrap" style="text-wrap: nowrap;">bilangan pokok 10</span> mudah dipakai dalam perhitungan manual dalam sistem bilangan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Desimal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Desimal">desimal</a>:<sup class="reference" id="cite_ref-7" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-7" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[6]</a></sup></p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ^{10}\!\log(10x)=\,^{10}\!\log 10+\,^{10}\!\log x=1+\,^{10}\!\log x.\ }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mo stretchy="false">(</mo><mn>10</mn><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>10</mn><mo>+</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mo>=</mo><mn>1</mn><mo>+</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mo>.</mo><mtext> </mtext></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ^{10}\!\log(10x)=\,^{10}\!\log 10+\,^{10}\!\log x=1+\,^{10}\!\log x.\ }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/368e085b4ea04af2ed356bdab1d53a726abc3cc6" style="border: 0px; display: inline-block; height: 3.176ex; vertical-align: -0.838ex; width: 46.817ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Jadi, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;">10</sup>log <i>x</i></span> berkaitan dengan jumlah <a href="https://id.wikipedia.org/wiki/Digit" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Digit">digit desimal</a> dari bilangan bulat positif <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>: jumlah digitnya merupakan <a href="https://id.wikipedia.org/wiki/Bilangan_bulat" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan bulat">bilangan bulat</a> terkecil yang lebih besar dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;">10</sup>log <i>x</i></span>.<sup class="reference" id="cite_ref-8" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-8" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[7]</a></sup> Sebagai contoh, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;">10</sup>log 1430</span> kira-kira sama dengan 3,15. Bilangan berikutnya merupakan jumlah digit dari 1430, yaitu 4. Dalam <a href="https://id.wikipedia.org/wiki/Teori_informasi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teori informasi">teori informasi</a>, logaritma alami dipakai dalam <a class="new" href="https://id.wikipedia.org/w/index.php?title=Nat_(unit)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Nat (unit) (halaman belum tersedia)">nat</a> dan logaritma dengan bilangan pokok 2 dipakai dalam <a class="mw-disambig" href="https://id.wikipedia.org/wiki/Bit" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bit">bit</a> sebagai satuan dasar informasi.<sup class="reference" id="cite_ref-9" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-9" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[8]</a></sup> Logaritma biner juga dipakai dalam <a href="https://id.wikipedia.org/wiki/Ilmu_komputer" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Ilmu komputer">ilmu komputer</a>, dengan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Sistem_biner" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Sistem biner">sistem biner</a> ditemukan dimana-mana. Dalam <a href="https://id.wikipedia.org/wiki/Teori_musik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teori musik">teori musik</a>, rasio tinggi nada kedua (yaitu <a href="https://id.wikipedia.org/wiki/Oktaf" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Oktaf">oktaf</a>) ditemukan dimana-mana dan jumlah <a href="https://id.wikipedia.org/wiki/Sen_(musik)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Sen (musik)">sen</a> antara setiap dua tinggi nada dirumuskan sebagai konstanta 1200 dikali logaritma dari rasio (yaitu, 100 sen per <a href="https://id.wikipedia.org/wiki/Setengah_nada" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Setengah nada">setengah nada</a> dengan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Temperamen_sama&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Temperamen sama (halaman belum tersedia)">temperamen sama</a>). Dalam <a href="https://id.wikipedia.org/wiki/Fotografi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fotografi">fotografi</a>, logaritma dengan bilangan pokok dua dipakai untuk mengukur <a href="https://id.wikipedia.org/wiki/Nilai_pajanan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Nilai pajanan">nilai pajanan</a>, <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Luminans" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Luminans">tingkatan cahaya</a>, <a href="https://id.wikipedia.org/wiki/Kecepatan_rana" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kecepatan rana">waktu eksposur</a>, <a href="https://id.wikipedia.org/wiki/Tingkap" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Tingkap">tingkap</a>, dan <a href="https://id.wikipedia.org/wiki/Kecepatan_film" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kecepatan film">kecepatan film</a> dalam "stop".<sup class="reference" id="cite_ref-10" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-10" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[9]</a></sup></p><p style="margin: 0.5em 0px 1em;">Tabel berikut memuat notasi-notasi umum mengenai bilangan pokok beserta bidang yang dipakai. Selain <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log <i>x</i></span>, adapula notasi logaritma lain yang ditulis sebagai <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log<sub style="font-size: 13.216px; line-height: 1;"><i>b</i></sub> <i>x</i></span>, dan juga seperti <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log <i>x</i></span>. Pada kolom "Notasi ISO" memuat penamaan yang disarankan <a href="https://id.wikipedia.org/wiki/Organisasi_Standardisasi_Internasional" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Organisasi Standardisasi Internasional">Organisasi Standardisasi Internasional</a>, yakni <a class="new" href="https://id.wikipedia.org/w/index.php?title=ISO_80000-2&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="ISO 80000-2 (halaman belum tersedia)">ISO 80000-2</a>.<sup class="reference" id="cite_ref-11" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-11" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[10]</a></sup> Karena notasi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log <span class="texhtml mvar" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">x</span></span> telah dipakai untuk ketiga bilangan pokok di atas (atau ketika bilangan pokok belum ditentukan), bilangan pokok yang dimaksud harus sering diduga tergantung konteks atau bidangnya. Sebagai contoh, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log</span> biasanya mengacu pada <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;">2</sup>log</span> dalam ilmu komputer, dan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log</span> mengacu pada <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>e</i></sup>log</span>.<sup class="reference" id="cite_ref-12" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-12" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[11]</a></sup> Dalam konteks lainnya, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log</span> seringkali mengacu pada <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;">10</sup>log</span>.<sup class="reference" id="cite_ref-13" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-13" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[12]</a></sup></p><table class="wikitable" style="background-color: #f8f9fa; border-collapse: collapse; border: 1px solid rgb(162, 169, 177); color: #202122; font-size: 14px; margin: 1em auto; text-align: center;"><tbody><tr><th scope="col" style="background-color: #eaecf0; border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em; text-align: center;">Bilangan pokok<p style="margin: 0.5em 0px 1em;"><span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span></p></th><th scope="col" style="background-color: #eaecf0; border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em; text-align: center;">Nama <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log <i>x</i></span></th><th scope="col" style="background-color: #eaecf0; border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em; text-align: center;">Notasi ISO</th><th scope="col" style="background-color: #eaecf0; border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em; text-align: center;">Notasi lain</th><th scope="col" style="background-color: #eaecf0; border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em; text-align: center;">Dipakai dalam bidang</th></tr><tr><th scope="row" style="background-color: #eaecf0; border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em; text-align: center;">2</th><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><a href="https://id.wikipedia.org/wiki/Logaritma_biner" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma biner">logaritma biner</a></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">lb <i>x</i></span><sup class="reference" id="cite_ref-gullberg_14-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-gullberg-14" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[13]</a></sup></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ld <i>x</i></span>, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log <i>x</i></span>, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">lg <i>x</i></span>,<sup class="reference" id="cite_ref-15" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-15" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[14]</a></sup> <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;">2</sup>log <i>x</i></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><a href="https://id.wikipedia.org/wiki/Ilmu_komputer" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Ilmu komputer">ilmu komputer</a>, <a href="https://id.wikipedia.org/wiki/Teori_informasi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teori informasi">teori informasi</a>, <a href="https://id.wikipedia.org/wiki/Bioinformatika" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bioinformatika">bioinformatika</a>, <a href="https://id.wikipedia.org/wiki/Teori_musik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teori musik">teori musik</a>, <a href="https://id.wikipedia.org/wiki/Fotografi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fotografi">fotografi</a></td></tr><tr><th scope="row" style="background-color: #eaecf0; border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em; text-align: center;"><span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">e</span></th><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><a href="https://id.wikipedia.org/wiki/Logaritma_alami" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma alami">logaritma alami</a></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln <i>x</i></span><sup class="reference" id="cite_ref-adaa_19-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-adaa-19" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[nb 2]</a></sup></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log <span class="texhtml mvar" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">x</span></span> (dipakai dalam matematika<sup class="reference" id="cite_ref-20" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-20" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[18]</a></sup> dan beberapa <a href="https://id.wikipedia.org/wiki/Bahasa_pemrograman" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bahasa pemrograman">bahasa pemrograman</a> lainnya<sup class="reference" id="cite_ref-21" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-21" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[nb 3]</a></sup>), <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>e</i></sup>log <i>x</i></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;">matematika, fisika, kimia,<p style="margin: 0.5em 0px 1em;"><a href="https://id.wikipedia.org/wiki/Statistik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Statistik">statistik</a>, <a href="https://id.wikipedia.org/wiki/Ekonomi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Ekonomi">ekonomi</a>, teori informasi, dan rekayasa</p></td></tr><tr><th scope="row" style="background-color: #eaecf0; border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em; text-align: center;">10</th><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><a class="mw-redirect" href="https://id.wikipedia.org/wiki/Logaritma_biasa" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma biasa">logaritma biasa</a></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">lg <i>x</i></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log <i>x</i></span>, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;">10</sup>log <i>x</i></span><p style="margin: 0.5em 0px 1em;">(dipakai dalam rekayasa, biologi, dan astronomi)</p></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;">bidang berbagai <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Rekayasa" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Rekayasa">rekayasa</a> (lihat <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Decibel" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Decibel">desibel</a> dan lihat di bawah),<p style="margin: 0.5em 0px 1em;"><a class="mw-redirect mw-disambig" href="https://id.wikipedia.org/wiki/Tabel" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Tabel">tabel</a> logaritma, <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Kalkulator" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kalkulator">kalkulator</a> genggam, <a href="https://id.wikipedia.org/wiki/Spektroskopi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Spektroskopi">spektroskopi</a></p></td></tr><tr><th scope="row" style="background-color: #eaecf0; border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em; text-align: center;"><span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span></th><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;">logaritma dengan bilangan pokok <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log <i>x</i></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;">matematika</td></tr></tbody></table><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Sejarah">Sejarah</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=7" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Sejarah">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=7" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Sejarah">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><div class="hatnote navigation-not-searchable" role="note" style="font-style: italic; margin-bottom: 0.5em; padding-left: 1.6em;">Artikel utama: <a href="https://id.wikipedia.org/wiki/Sejarah_logaritma" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Sejarah logaritma">Sejarah logaritma</a></div><p style="margin: 0.5em 0px 1em;"><b>Sejarah logaritma</b> yang dimulai dari Eropa pada abad ketujuh belas merupakan penemuan <a href="https://id.wikipedia.org/wiki/Fungsi_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi (matematika)">fungsi</a> terbaru yang memperluas dunia analisis di luar keterbatasan metode aljabar. Metode logaritma dikemukakan secara terbuka oleh <a href="https://id.wikipedia.org/wiki/John_Napier" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="John Napier">John Napier</a> pada tahun 1614, dalam bukunya yang berjudul <i><a href="https://id.wikipedia.org/wiki/Mirifici_Logarithmorum_Canonis_Descriptio" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Mirifici Logarithmorum Canonis Descriptio">Mirifici Logarithmorum Canonis Descriptio</a></i>.<sup class="reference" id="cite_ref-22" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-22" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[19]</a></sup><sup class="reference" id="cite_ref-23" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-23" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[20]</a></sup> Namun, teknik-teknik lain sebelum penemuan Napier sudah ada dengan keterbatasan metode yang serupa, contohnya seperti <a href="https://id.wikipedia.org/wiki/Prosthafaeresis" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Prosthafaeresis">prosthafaeresis</a> atau penggunaan tabel barisan, yang dikembangkan dengan luas oleh <a href="https://id.wikipedia.org/wiki/Jost_B%C3%BCrgi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Jost Bürgi">Jost Bürgi</a> sekitar tahun 1600.<sup class="reference" id="cite_ref-folkerts_24-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-folkerts-24" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[21]</a></sup><sup class="reference" id="cite_ref-25" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-25" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[22]</a></sup> Napier menciptakan istilah untuk logaritma dalam bahasa Latin Tengah, “logaritmus”, yang berasal dari gabungan dua kata Yunani, <i>logos</i> “proporsi, rasio, kata” + <i>arithmos</i> “bilangan”. Secara harfiah, "logaritmus" berarti “bilangan rasio”.</p><p style="margin: 0.5em 0px 1em;"><a href="https://id.wikipedia.org/wiki/Logaritma_umum" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma umum">Logaritma umum</a> dari bilangan adalah indeks dari perpangkatan sepuluh yang sama dengan bilangan tersebut.<sup class="reference" id="cite_ref-26" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-26" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[23]</a></sup> Bilangan yang sangat membutuhkan banyak angka merupakan kiasan kasar untuk logaritma umum, dan <a href="https://id.wikipedia.org/wiki/Archimedes" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Archimedes">Archimedes</a> menyebutnya sebagai “orde bilangan”.<sup class="reference" id="cite_ref-27" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-27" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[24]</a></sup> Logaritma real pertama adalah metode heuristik yang mengubah perkalian menjadi penjumlahan, sehingga memudahkan perhitungan yang cepat. Ada beberapa metode yang menggunakan tabel yang diperoleh dari identitas trigonometri,<sup class="reference" id="cite_ref-28" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-28" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[25]</a></sup> dan metode tersebut dinamakan <a href="https://id.wikipedia.org/wiki/Prosthafaeresis" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Prosthafaeresis">prosthafaeresis</a>.</p><p style="margin: 0.5em 0px 1em;">Penemuan <a href="https://id.wikipedia.org/wiki/Fungsi_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi (matematika)">fungsi</a> yang dikenal saat ini sebagai <a href="https://id.wikipedia.org/wiki/Logaritma_alami" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma alami">logaritma alami</a>, berawal dari saat <a href="https://id.wikipedia.org/wiki/Gr%C3%A9goire_de_Saint-Vincent" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Grégoire de Saint-Vincent">Grégoire de Saint-Vincent</a> mencoba menggambarkan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Kuadratur_(matematika)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Kuadratur (matematika) (halaman belum tersedia)">kuadratur</a> <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Hiperbola" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Hiperbola">hiperbola</a> persegi panjang. Archimedes menulis risalah yang berjudul <i><a href="https://id.wikipedia.org/wiki/Quadrature_of_the_Parabola" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Quadrature of the Parabola">The Quadrature of the Parabola</a></i> pada abad ke-3 SM, tetapi kuadratur hiperbola menghindari semua upayanya hingga Saint-Vincent menerbitkan hasilnya pada tahun 1647. Logaritma yang mengaitkan <a href="https://id.wikipedia.org/wiki/Barisan_dan_deret_geometri" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Barisan dan deret geometri">barisan dan deret geometri</a> dalam <a class="new" href="https://id.wikipedia.org/w/index.php?title=Argumen_dari_fungsi&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Argumen dari fungsi (halaman belum tersedia)">argumen</a> dan nilai <a href="https://id.wikipedia.org/wiki/Barisan_dan_deret_aritmetika" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Barisan dan deret aritmetika">barisan dan deret aritmetika</a>, meminta <a class="mw-redirect" href="https://id.wikipedia.org/wiki/A._A._de_Sarasa" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="A. A. de Sarasa">Antonio de Sarasa</a> untuk mengaitkan kuadratur Saint-Vincent dan tradisi logaritma dalam <a href="https://id.wikipedia.org/wiki/Prosthafaeresis" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Prosthafaeresis">prosthafaeresis</a> sehingga mengarah ke sebuah persamaan kata untuk logaritma alami, yaitu "logaritma hiperbolik". <a href="https://id.wikipedia.org/wiki/Christiaan_Huygens" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Christiaan Huygens">Christiaan Huygens</a> dan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/James_Gregory_(matematikawan)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="James Gregory (matematikawan)">James Gregory</a> mulai mengenali fungsi baru tersebut. <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Gottfried Wilhelm Leibniz">Leibniz</a> memakai notasi Log y pada tahun 1675,<sup class="reference" id="cite_ref-29" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-29" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[26]</a></sup> dan tahun berikutnya ia mengaitkannya dengan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Kalkulus_integral" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kalkulus integral">integral</a></p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \int {\frac {dy}{y}}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>∫</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi>�</mi><mi>�</mi></mrow><mi>�</mi></mfrac></mrow><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \int {\frac {dy}{y}}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2507ed996fea98453b8d7bccdcd25cfc0295076" style="border: 0px; display: inline-block; height: 5.843ex; vertical-align: -2.338ex; width: 6.435ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Sebelum Euler mengembangkan konsep modernnya tentang logaritma alami kompleks, <a href="https://id.wikipedia.org/wiki/Roger_Cotes#Matematika" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Roger Cotes">Roger Cotes</a> memperlihatkan hasil yang hampir sama pada tahun 1714 bahwa<sup class="reference" id="cite_ref-30" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-30" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[27]</a></sup></p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \log(\cos \theta +i\sin \theta )=i\theta }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>log</mi><mo></mo><mo stretchy="false">(</mo><mi>cos</mi><mo></mo><mi>�</mi><mo>+</mo><mi>�</mi><mi>sin</mi><mo></mo><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><mi>�</mi><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \log(\cos \theta +i\sin \theta )=i\theta }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bce998fc2c1339694373e030f0ef02964dd7dc6" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.838ex; width: 22.724ex;" /></span>.</dd></dl><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span id="Tabel_logaritma.2C_mistar_hitung.2C_dan_penerapan_bersejarah"></span><span class="mw-headline" id="Tabel_logaritma,_mistar_hitung,_dan_penerapan_bersejarah">Tabel logaritma, mistar hitung, dan penerapan bersejarah</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=8" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Tabel logaritma, mistar hitung, dan penerapan bersejarah">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=8" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Tabel logaritma, mistar hitung, dan penerapan bersejarah">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><figure class="mw-halign-right" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Logarithms_Britannica_1797.png" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img class="mw-file-element" data-file-height="354" data-file-width="997" decoding="async" height="128" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/82/Logarithms_Britannica_1797.png/360px-Logarithms_Britannica_1797.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Logarithms_Britannica_1797.png/540px-Logarithms_Britannica_1797.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/82/Logarithms_Britannica_1797.png/720px-Logarithms_Britannica_1797.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="360" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Penjelasan logaritma dalam <i><a href="https://id.wikipedia.org/wiki/Encyclop%C3%A6dia_Britannica" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Encyclopædia Britannica">Encyclopædia Britannica</a></i> pada tahun 1797.</figcaption></figure><p style="margin: 0.5em 0px 1em;">Dengan menyederhanakan perhitungan yang rumit sebelum adanya mesin hitung komputer, logaritma berkontribusi pada kemajuan pengetahuan, khususnya <a href="https://id.wikipedia.org/wiki/Astronomi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Astronomi">astronomi</a>. Logaritma sangat penting terhadap kemajuan dalam <a href="https://id.wikipedia.org/wiki/Ilmu_ukur_wilayah" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Ilmu ukur wilayah">survei</a>, <a href="https://id.wikipedia.org/wiki/Navigasi_benda_langit" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Navigasi benda langit">navigasi benda langit</a>, dan cabang lainnya. <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Pierre-Simon_Laplace" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Pierre-Simon Laplace">Pierre-Simon Laplace</a> menyebut logaritma sebagai</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;">"...kecerdasan yang mengagumkan, [sebuah alat] yang mengurangi pekerjaan berbulan-bulan menjadi beberapa hari, menggandakan kehidupan astronom, dan menghindarinya dari kesalahan dan rasa jijik yang tak terpisahkan dari perhitungan yang panjang."<sup class="reference" id="cite_ref-31" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-31" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[28]</a></sup></dd></dl></dd></dl><p style="margin: 0.5em 0px 1em;"><span id="Antilogaritma"></span>Karena fungsi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f</i>(<i>x</i>) = <span class="texhtml mvar" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">b</span><sup style="font-size: 13.216px; line-height: 1;"><i>x</i></sup></span> adalah fungsi invers dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log <i>x</i></span>, maka fungsi tersebut disebut sebagai <b>antilogaritma</b>.<sup class="reference" id="cite_ref-32" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-32" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[29]</a></sup> Saat ini, antilogaritma lebih sering disebut <a href="https://id.wikipedia.org/wiki/Fungsi_eksponensial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi eksponensial">fungsi eksponensial</a>.</p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Tabel_logaritma">Tabel logaritma</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=9" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Tabel logaritma">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=9" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Tabel logaritma">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;">Sebuah alat penting yang memungkinkan penggunaan logaritma adalah <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Tabel_logaritma" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Tabel logaritma">tabel logaritma</a>.<sup class="reference" id="cite_ref-33" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-33" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[30]</a></sup> Tabel logaritma pertama kali disusun oleh <a href="https://id.wikipedia.org/wiki/Henry_Briggs_(matematikawan)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Henry Briggs (matematikawan)">Henry Briggs</a> pada tahun 1617 setelah penemuan Napier, tetapi penemuannya menggunakan 10 sebagai bilangan pokok. Tabel pertamanya memuat <a href="https://id.wikipedia.org/wiki/Logaritma_umum" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma umum">logaritma umum</a> dari semua bilangan bulat yang berkisar antara 1 dengan 1000, dengan ketepatan yang dimiliki 14 digit, dan kemudian ia membuat tabel dengan kisaran yang besar. Tabel tersebut mencantumkan nilai <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ^{10}\!\log x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ^{10}\!\log x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/802977eb401f38616d7885ca853c5c2cc89b2dc0" style="border: 0px; display: inline-block; height: 3.009ex; margin: 0px; vertical-align: -0.671ex; width: 6.565ex;" /></span> untuk setiap bilangan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" style="border: 0px; display: inline-block; height: 1.676ex; margin: 0px; vertical-align: -0.338ex; width: 1.33ex;" /></span> dalam kisaran dan ketepatan tertentu. Karena bilangan yang berbeda dengan faktor 10 memiliki logaritma yang berbeda dengan bilangan bulat, logaritma dengan bilangan pokok 10 digunakan secara universal untuk perhitungan, sehingga disebut logaritma umum. Logaritma umum dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" style="border: 0px; display: inline-block; height: 1.676ex; margin: 0px; vertical-align: -0.338ex; width: 1.33ex;" /></span> dipisahkan menjadi <a href="https://id.wikipedia.org/wiki/Fungsi_bilangan_bulat_terbesar_dan_terkecil" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi bilangan bulat terbesar dan terkecil">bagian bilangan bulat</a> yang dikenal sebagai karakteristik, dan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Bagian_pecahan&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Bagian pecahan (halaman belum tersedia)">bagian pecahan</a> (<a href="https://id.wikipedia.org/wiki/Bahasa_Inggris" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bahasa Inggris">bahasa Inggris</a>: <span lang="en"><i>fractional part</i></span>) yang dikenal sebagai <a href="https://id.wikipedia.org/wiki/Logaritma_umum#Mantissa_dan_karakteristiknya" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma umum">mantissa</a>. Tabel logaritma hanya perlu menyertakan mantissa, karena karakteristik logaritma umum dapat dengan mudah ditentukan dengan menghitung angka dari titik desimal.<sup class="reference" id="cite_ref-34" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-34" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[31]</a></sup> Karakteristik logaritma umum dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 10\cdot x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>10</mn><mo>⋅</mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 10\cdot x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8fa3f94271366f77c0dd17d8074260b749a5799" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 5.334ex;" /></span> sama dengan satu ditambah karakteristik <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" style="border: 0px; display: inline-block; height: 1.676ex; margin: 0px; vertical-align: -0.338ex; width: 1.33ex;" /></span>, dan mantissanya sama. Dengan menggunakan tabel logartima dengan tiga digit, nilai logaritma dari 3542 kira-kira sama dengan</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ^{10}\!\log 3542=\,^{10}\!\log(1000\cdot 3,542)=3+\,^{10}\!\log 3,542\approx 3+\,^{10}\!\log 3,54}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>3542</mn><mo>=</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mo stretchy="false">(</mo><mn>1000</mn><mo>⋅</mo><mn>3</mn><mo>,</mo><mn>542</mn><mo stretchy="false">)</mo><mo>=</mo><mn>3</mn><mo>+</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>3</mn><mo>,</mo><mn>542</mn><mo>≈</mo><mn>3</mn><mo>+</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>3</mn><mo>,</mo><mn>54</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ^{10}\!\log 3542=\,^{10}\!\log(1000\cdot 3,542)=3+\,^{10}\!\log 3,542\approx 3+\,^{10}\!\log 3,54}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bdb1d0975b2e2376db520c16d04baccaa1de6bf8" style="border: 0px; display: inline-block; height: 3.176ex; vertical-align: -0.838ex; width: 67.692ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Nilainya dengan ketepatan yang sangat tinggi dapat diperoleh melalui <a class="mw-disambig" href="https://id.wikipedia.org/wiki/Interpolasi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Interpolasi">interpolasi</a>:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ^{10}\!\log 3542\approx 3+^{10}\!\log 3,54+0,2\cdot (\,^{10}\!\log 3,55-\,^{10}\!\log 3,54)}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>3542</mn><mo>≈</mo><mn>3</mn><msup><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>3</mn><mo>,</mo><mn>54</mn><mo>+</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>⋅</mo><mo stretchy="false">(</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>3</mn><mo>,</mo><mn>55</mn><mo>−</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mn>3</mn><mo>,</mo><mn>54</mn><mo stretchy="false">)</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ^{10}\!\log 3542\approx 3+^{10}\!\log 3,54+0,2\cdot (\,^{10}\!\log 3,55-\,^{10}\!\log 3,54)}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b05b164ba56940967f0698f9a0f0b6cff840c01" style="border: 0px; display: inline-block; height: 3.176ex; vertical-align: -0.838ex; width: 59.17ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Nilai <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 10^{x}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mn>10</mn><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 10^{x}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86f9a6c2de625bd03ffd20e1fa89dad13da52eaa" style="border: 0px; display: inline-block; height: 2.343ex; margin: 0px; vertical-align: -0.338ex; width: 3.497ex;" /></span> dapat ditentukan dengan pencarian terbalik pada tabel yang sama, karena logaritma merupakan <a href="https://id.wikipedia.org/wiki/Fungsi_monoton" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi monoton">fungsi monoton</a>.</p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Perhitungan">Perhitungan</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=10" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Perhitungan">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=10" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Perhitungan">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;">Hasil kali atau hasil bagi dari dua bilangan positif <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">c</span> dan <i><span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">d</span></i> biasanya dihitung sebagai penambahan dan pengurangan logaritma. Hasil kali <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>cd</i></span> berasal dari antilogaritma dari penambahan dan hasil bagi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><span class="sfrac nowrap" style="display: inline-block; font-size: 14.042px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;"><i>c</i></span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;"><i>d</i></span></span></span> berasal dari antilogaritma dari pengurangan, melalui tabel yang sama:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle cd=10^{\,^{10}\!\log c}\,10^{\,^{10}\!\log d}=10^{\,^{10}\!\log c\,+\,^{10}\!\log d}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mi>�</mi><mo>=</mo><msup><mn>10</mn><mrow class="MJX-TeXAtom-ORD"><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mrow></msup><mspace width="thinmathspace"></mspace><msup><mn>10</mn><mrow class="MJX-TeXAtom-ORD"><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mrow></msup><mo>=</mo><msup><mn>10</mn><mrow class="MJX-TeXAtom-ORD"><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mspace width="thinmathspace"></mspace><mo>+</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle cd=10^{\,^{10}\!\log c}\,10^{\,^{10}\!\log d}=10^{\,^{10}\!\log c\,+\,^{10}\!\log d}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a2f41a5f4ad0ab5c5c0601e332d11283d4eaecb" style="border: 0px; display: inline-block; height: 3.009ex; vertical-align: -0.338ex; width: 38.785ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">dan</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\frac {c}{d}}=cd^{-1}=10^{\,^{10}\!\log c\,-\,^{10}\!\log d}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow><mo>=</mo><mi>�</mi><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><mo>=</mo><msup><mn>10</mn><mrow class="MJX-TeXAtom-ORD"><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mspace width="thinmathspace"></mspace><mo>−</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mrow></msup><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\frac {c}{d}}=cd^{-1}=10^{\,^{10}\!\log c\,-\,^{10}\!\log d}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/762963139558dcd41a87e55771d55125591dfef1" style="border: 0px; display: inline-block; height: 4.843ex; vertical-align: -2.005ex; width: 27.997ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Untuk perhitungan manual yang meminta ketelitian yang cukup besar, melakukan pencarian kedua logaritma, menghitung jumlah atau selisihnya, dan mencari antilogaritma jauh lebih cepat daripada menghitung perkalian dengan metode sebelumnya seperti <a href="https://id.wikipedia.org/wiki/Prosthafaeresis" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Prosthafaeresis">prosthafaeresis</a>, yang mengandalkan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Identitas_trigonometri" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Identitas trigonometri">identitas trigonometri</a>.</p><p style="margin: 0.5em 0px 1em;">Perhitungan pangkat direduksi menjadi perkalian, dan sedangkan perhitungan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Akar_ke-n" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Akar ke-n">akar</a> direduksi menjadi pembagian. Pernyataan ini dapat dilihat sebagai</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle c^{d}=\left(10^{\,^{10}\!\log c}\right)^{d}=10^{\,d\,^{10}\!\log c}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>=</mo><msup><mrow><mo>(</mo><msup><mn>10</mn><mrow class="MJX-TeXAtom-ORD"><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mrow></msup><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>=</mo><msup><mn>10</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace"></mspace><mi>�</mi><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle c^{d}=\left(10^{\,^{10}\!\log c}\right)^{d}=10^{\,d\,^{10}\!\log c}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ca24b60d8c2e2e228133cc80765d8ee9e33cef2" style="border: 0px; display: inline-block; height: 5.343ex; vertical-align: -1.838ex; width: 28.697ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">dan</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\sqrt[{d}]{c}}=c^{\frac {1}{d}}=10^{{\frac {1}{d}}\,^{10}\!\log c}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mroot><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></mroot></mrow><mo>=</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mi>�</mi></mfrac></mrow></msup><mo>=</mo><msup><mn>10</mn><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mi>�</mi></mfrac></mrow><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mrow></msup><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\sqrt[{d}]{c}}=c^{\frac {1}{d}}=10^{{\frac {1}{d}}\,^{10}\!\log c}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e30502b2965ed055a829e5a3eddbcb4afb79ef8d" style="border: 0px; display: inline-block; height: 4.176ex; vertical-align: -1.005ex; width: 21.737ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Perhitungan trigonometri dilengkapi dengan tabel-tabel yang memuat logaritma umum dari <a href="https://id.wikipedia.org/wiki/Fungsi_trigonometri" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi trigonometri">fungsi trigonometri</a>.</p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Mistar_hitung">Mistar hitung</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=11" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Mistar hitung">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=11" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Mistar hitung">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;">Penerapan penting lainnya adalah <a href="https://id.wikipedia.org/wiki/Mistar_hitung" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Mistar hitung">mistar hitung</a>, sepasang skala yang dibagi secara logaritmik yang digunakan dalam perhitungan. Adapun skala logaritmik yang tidak memiliki sorong, <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Mistar_Gunter" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Mistar Gunter">mistar Gunter</a>, ditemukan tak lama setelah penemuan Napier dan disempurnakan oleh <a href="https://id.wikipedia.org/wiki/William_Oughtred" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="William Oughtred">William Oughtred</a> untuk menciptakan sepasang skala logaritmik yang dapat dipindahkan terhadap satu sama lain, yaitu mistar hitung. Angka yang ditempatkan pada skala hitung pada jarak sebanding dengan selisih antara logaritmanya. Menggeser skala atas dengan tepat berarti menambahkan logaritma secara mekanis, seperti yang diilustrasikan berikut ini:</p><figure class="mw-halign-center" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: none; display: table; float: none; line-height: 0; margin: 0px auto 0.5em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Slide_rule_example2_with_labels.svg" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img alt="alt=A slide rule: two rectangles with logarithmically ticked axes, arrangement to add the distance from 1 to 2 to the distance from 1 to 3, indicating the product 6." class="mw-file-element" data-file-height="119" data-file-width="512" decoding="async" height="128" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Slide_rule_example2_with_labels.svg/550px-Slide_rule_example2_with_labels.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Slide_rule_example2_with_labels.svg/825px-Slide_rule_example2_with_labels.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Slide_rule_example2_with_labels.svg/1100px-Slide_rule_example2_with_labels.svg.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="550" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Penggambaran skema mengenai mistar hitung. Dimulai dari 2 pada skala di bawah, lalu tambahkan dengan jarak ke 3 pada skala atas agar mencapai hasil kali 6. Mistar hitung bekerja karena ditandai sedemikian rupa sehingga jarak dari 1 ke <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>x</i></span> sebanding dengan logaritma <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>x</i></span>.</figcaption></figure><p style="margin: 0.5em 0px 1em;">Sebagai contoh, dengan menambahkan jarak dari 1 ke 2 pada skala di bagian bawah ke jarak dari 1 ke 3 pada skala di bagian atas menghasilkan hasil kali 6, yang dibacakan di bagian bawah. Mistar hitung adalah sebuah alat menghitung yang penting bagi para insinyur dan ilmuwan hingga tahun 1970-an, karena dengan mengorbankan ketepatan nilai memungkinkan perhitungan yang jauh lebih cepat daripada teknik berdasarkan tabel.<sup class="reference" id="cite_ref-ReferenceA2_35-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-ReferenceA2-35" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[32]</a></sup></p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Sifat_analitik">Sifat analitik</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=12" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Sifat analitik">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=12" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Sifat analitik">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><p style="margin: 0.5em 0px 1em;">Kajian yang lebih dalam mengenai logaritma memerlukan sebuah konsep yang disebut <i><a href="https://id.wikipedia.org/wiki/Fungsi_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi (matematika)">fungsi</a></i>. Fungsi merupakan sebuah kaidah yang dipetakan suatu bilangan akan menghasilkan bilangan lain.<sup class="reference" id="cite_ref-36" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-36" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[33]</a></sup> Contohnya seperti fungsi yang menghasilkan bilangan konstan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span>, yang dipangkatkan setiap bilangan real <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>. Fungsi ini secara matematis ditulis sebagai <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f</i>(<i>x</i>) = <span class="texhtml mvar" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">b</span><sup style="font-size: 13.216px; line-height: 1;"> <i>x</i></sup></span>. Ketika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> positif dan tak sama dengan 1, maka <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">f</span> adalah fungsi terbalikkan ketika dianggap sebagai fungsi dengan interval dari bilangan real ke bilangan real positif.</p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Keberadaan">Keberadaan</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=13" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Keberadaan">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=13" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Keberadaan">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;">Misalkan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> adalah bilangan real positif yang tidak sama dengan 1 dan misalkan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f</i>(<i>x</i>) = <span class="texhtml mvar" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">b</span><sup style="font-size: 13.216px; line-height: 1;"> <i>x</i></sup></span>. Pernyataan yang diikuti dari <a href="https://id.wikipedia.org/wiki/Teorema_nilai_antara" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teorema nilai antara">teorema nilai antara</a> ini,<sup class="reference" id="cite_ref-LangIII.3_37-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-LangIII.3-37" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[34]</a></sup> merupakan hasil standar dalam analisis real yang mengatakan bahwa setiap fungsi monoton sempurna dan kontinu merupakan fungsi bijektif antara ranah (<a href="https://id.wikipedia.org/wiki/Bahasa_Inggris" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bahasa Inggris">bahasa Inggris</a>: <span lang="en"><i>domain</i></span>) dan kisarannya (<a href="https://id.wikipedia.org/wiki/Bahasa_Inggris" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bahasa Inggris">bahasa Inggris</a>: <span lang="en"><i>range</i></span>). Pernyataan saat ini mengatakan bahwa <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">f</span> yang <a href="https://id.wikipedia.org/wiki/Fungsi_monoton" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi monoton">menaik sempurna</a> (untuk <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i> > 1</span>), atau menurun sempurna (untuk <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">0 < <span class="texhtml mvar" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">b</span> < 1</span>)<sup class="reference" id="cite_ref-LangIV.2_38-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-LangIV.2-38" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[35]</a></sup> merupakan fungsi kontinu, memiliki ranah <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 1.678ex;" /></span> dan memiliki kisaran <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} _{>0}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mo>></mo><mn>0</mn></mrow></msub></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} _{>0}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/731b0a191e1eb70161af731d0d567b236457074f" style="border: 0px; display: inline-block; height: 2.509ex; margin: 0px; vertical-align: -0.671ex; width: 4.011ex;" /></span>. Oleh karena itu, <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">f</span> adalah fungsi bijeksi dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 1.678ex;" /></span> ke <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathbb {R} _{>0}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mo>></mo><mn>0</mn></mrow></msub></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathbb {R} _{>0}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/731b0a191e1eb70161af731d0d567b236457074f" style="border: 0px; display: inline-block; height: 2.509ex; margin: 0px; vertical-align: -0.671ex; width: 4.011ex;" /></span>. Dengan kata lain, untuk setiap bilangan real positif <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span>, terdapat setidaknya satu bilangan real <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> sehingga <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle b^{x}=y}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>=</mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle b^{x}=y}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/711753605e98f4d42b75fe61254c3b8f311a5fd3" style="border: 0px; display: inline-block; height: 2.676ex; margin: 0px; vertical-align: -0.671ex; width: 6.424ex;" /></span>.</p><p style="margin: 0.5em 0px 1em;">Misalkan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ^{b}\!\log \colon \mathbb {R} _{>0}\to \mathbb {R} }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo>:</mo><msub><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mo>></mo><mn>0</mn></mrow></msub><mo stretchy="false">→</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">�</mi></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ^{b}\!\log \colon \mathbb {R} _{>0}\to \mathbb {R} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31746391b5062e64d57274565c0222a75f19d1bd" style="border: 0px; display: inline-block; height: 3.009ex; margin: 0px; vertical-align: -0.671ex; width: 14.246ex;" /></span> yang menyatakan invers dari fungsi <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">f</span>. Dalam artian, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log <i>y</i></span> adalah bilangan real tunggal <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> sehingga <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle b^{x}=y}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>=</mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle b^{x}=y}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/711753605e98f4d42b75fe61254c3b8f311a5fd3" style="border: 0px; display: inline-block; height: 2.676ex; margin: 0px; vertical-align: -0.671ex; width: 6.424ex;" /></span>. Fungsi ini disebut <i>fungsi logaritma</i> dengan bilangan pokok-<span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> atau <i>fungsi logaritmik</i> (atau <i>logaritma</i> saja).</p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Karakterisasi_melalui_rumus_hasil_kali">Karakterisasi melalui rumus hasil kali</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=14" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Karakterisasi melalui rumus hasil kali">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=14" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Karakterisasi melalui rumus hasil kali">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;">Pada dasarnya, fungsi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log <i>x</i></span> juga dapat dikarakterisasikan melalui rumus hasil kali</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ^{b}\!\log(xy)=\,^{b}\!\log x+\,^{b}\!\log y.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mo>+</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ^{b}\!\log(xy)=\,^{b}\!\log x+\,^{b}\!\log y.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ef6ca6c34ac8d98ecd0191a3e7d080011ad3b94" style="border: 0px; display: inline-block; height: 3.176ex; vertical-align: -0.838ex; width: 26.642ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Lebih tepatnya, logaritma untuk setiap bilangan pokok <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i> > 1</span> yang hanya merupakan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Fungsi_menaik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi menaik">fungsi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f</i></span> naik</a> dari bilangan real positif ke bilangan real memenuhi sifat bahwa <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f</i>(<i>b</i>) = 1</span> dan<sup class="reference" id="cite_ref-39" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-39" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[36]</a></sup></p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle f(xy)=f(x)+f(y).}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>+</mo><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle f(xy)=f(x)+f(y).}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ee6f0eb6e355d16f673a0d4a21705e24a227008" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.838ex; width: 20.82ex;" /></span></dd></dl><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Grafik_fungsi_logaritma">Grafik fungsi logaritma</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=15" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Grafik fungsi logaritma">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=15" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Grafik fungsi logaritma">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><figure class="mw-default-size mw-halign-right" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Logarithm_inversefunctiontoexp.svg" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img alt="The graphs of two functions." class="mw-file-element" data-file-height="279" data-file-width="240" decoding="async" height="256" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/49/Logarithm_inversefunctiontoexp.svg/220px-Logarithm_inversefunctiontoexp.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Logarithm_inversefunctiontoexp.svg/330px-Logarithm_inversefunctiontoexp.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/49/Logarithm_inversefunctiontoexp.svg/440px-Logarithm_inversefunctiontoexp.svg.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="220" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Grafik fungsi logaritma <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 11.6829px; line-height: 1;"><i>b</i></sup>log (<i>x</i>)</span> (berwarna biru) diperoleh dengan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Refleksi_(matematika)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Refleksi (matematika) (halaman belum tersedia)">mencerminkan</a> grafik fungsi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i><sup style="font-size: 11.6829px; line-height: 1;"><i>x</i></sup></span> (berwarna merah) di garis diagonal(<span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>x</i> = <span class="texhtml mvar" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">y</span></span>).</figcaption></figure><p style="margin: 0.5em 0px 1em;">Seperti yang dibahas sebelumnya, fungsi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log</span> invers terhadap fungsi eksponensial <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x\mapsto b^{x}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo stretchy="false">↦</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x\mapsto b^{x}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/873987f9618fe2c30ce4e72cbd1a967ff759c1d4" style="border: 0px; display: inline-block; height: 2.343ex; margin: 0px; vertical-align: -0.338ex; width: 7.114ex;" /></span>. Karena itu, <a href="https://id.wikipedia.org/wiki/Grafik_fungsi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Grafik fungsi">grafiknya</a> berkorespondensi dengan satu sama lain saat menukar koordinat-<span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> dan koordinat-<span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> (atau saat melakukan pencerminan di garis diagonal <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>x</i> = <i>y</i></span>), seperti yang diperlihatkan sebagai berikut: sebuah titik <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">(<i>t</i>, <i>u</i> = <span class="texhtml mvar" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">b</span><sup style="font-size: 13.216px; line-height: 1;"><i>t</i></sup>)</span> pada grafik dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">f</span> menghasilkan sebuah titik <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">(<i>u</i>, <i>t</i> = <sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log <i>u</i>)</span> pada grafik logaritma dan sebaliknya. Akibatnya, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log (<i>x</i>)</span> <a href="https://id.wikipedia.org/wiki/Limit_barisan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Limit barisan">divergen menuju takhingga</a> (dalam artian semakin besar dari setiap bilangan yang diberikan) jika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> naik menuju takhingga, asalkan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> lebih besar dari satu. Pada kasus tersebut, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log(<i>x</i>)</span> merupakan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Fungsi_menaik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi menaik">fungsi menaik</a>. Sedangkan untuk kasus <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i> < 1</span>, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log (<i>x</i>)</span> cenderung menuju ke negatif takhingga. Ketika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> mendekati nol, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log <i>x</i></span> menuju ke negatif takhingga untuk <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i> > 1</span> dan menuju ke plus takhingga untuk <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i> < 1</span>.</p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Turunan_dan_antiturunan">Turunan dan antiturunan</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=16" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Turunan dan antiturunan">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=16" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Turunan dan antiturunan">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><figure class="mw-halign-right" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Logarithm_derivative.svg" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img alt="Sebuah grafik fungsi logaritma dan sebuah garis yang menyinggungnya di sebuah titik." class="mw-file-element" data-file-height="243" data-file-width="375" decoding="async" height="143" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/57/Logarithm_derivative.svg/220px-Logarithm_derivative.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Logarithm_derivative.svg/330px-Logarithm_derivative.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/57/Logarithm_derivative.svg/440px-Logarithm_derivative.svg.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="220" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Grafik fungsi <a href="https://id.wikipedia.org/wiki/Logaritma_alami" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma alami">logaritma alami</a> (berwarna hijau) beserta garis singgungnya di <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>x</i> = 1,5</span> (berwarna hitam)</figcaption></figure><p style="margin: 0.5em 0px 1em;">Sifat analitik tentang fungsi adalah melalui fungsi inversnya.<sup class="reference" id="cite_ref-LangIII.3_37-1" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-LangIII.3-37" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[34]</a></sup> Jadi, ketika <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f</i>(<i>x</i>) = <span class="texhtml mvar" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">b</span><sup style="font-size: 13.216px; line-height: 1;"><i>x</i></sup></span> adalah fungsi kontinu dan <a href="https://id.wikipedia.org/wiki/Fungsi_terdiferensialkan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi terdiferensialkan">terdiferensialkan</a>, maka <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log <i>y</i></span> fungsi kontinu dan terdiferensialkan juga. Penjelasan kasarnya, sebuah fungsi kontinu adalah terdiferensialkan jika grafiknya tidak mempunyai "ujung" yang tajam. Lebih lanjut, ketika <a href="https://id.wikipedia.org/wiki/Turunan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan">turunan</a> dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f</i>(<i>x</i>)</span> menghitung nilai <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>b</i>) <i>b</i><sup style="font-size: 13.216px; line-height: 1;"><i>x</i></sup></span> melalui sifat-sifat <a href="https://id.wikipedia.org/wiki/Fungsi_eksponensial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi eksponensial">fungsi eksponensial</a>, <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Aturan_rantai" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Aturan rantai">aturan rantai</a> menyiratkan bahwa turunan dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log <i>x</i></span> dirumuskan sebagai <sup class="reference" id="cite_ref-LangIV.2_38-1" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-LangIV.2-38" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[35]</a></sup><sup class="reference" id="cite_ref-40" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-40" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[37]</a></sup></p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\frac {d}{dx}}\,^{b}\!\log x={\frac {1}{x\ln b}}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mi>�</mi><mi>�</mi></mrow></mfrac></mrow><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mrow><mi>�</mi><mi>ln</mi><mo></mo><mi>�</mi></mrow></mfrac></mrow><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\frac {d}{dx}}\,^{b}\!\log x={\frac {1}{x\ln b}}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01f9134d7ac023399f1a19b2ac1c37e308d07125" style="border: 0px; display: inline-block; height: 5.509ex; vertical-align: -2.005ex; width: 19.017ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Artinya, <a href="https://id.wikipedia.org/wiki/Kemiringan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kemiringan">kemiringan</a> dari <a href="https://id.wikipedia.org/wiki/Garis_singgung" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Garis singgung">garis singgung</a> yang menyinggung grafik logaritma dengan bilangan pokok <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>b</i></span> di titik <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">(<i>x</i>, <sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup>log (<i>x</i>))</span> sama dengan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><span class="sfrac nowrap" style="display: inline-block; font-size: 14.042px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;">1</span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;"><i>x</i> ln(<i>b</i>)</span></span></span>.</p><p style="margin: 0.5em 0px 1em;">Turunan dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>x</i>)</span> adalah <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><span class="sfrac nowrap" style="display: inline-block; font-size: 14.042px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;">1</span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;"><i>x</i></span></span></span>, yang berarti ini menyiratkan bahwa <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>x</i>)</span> adalah <a href="https://id.wikipedia.org/wiki/Integral" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Integral">integral</a> tunggal dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><span class="sfrac nowrap" style="display: inline-block; font-size: 14.042px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;">1</span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;"><i>x</i></span></span></span> yang mempunyai nilai 0 untuk <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>x</i> = 1</span>. Hal ini merupakan rumus paling sederhana yang mendorong sifat "alami" pada logaritma alami, dan hal ini juga merupakan salah satu alasan pentingnya konstanta <a href="https://id.wikipedia.org/wiki/E_(konstanta_matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="E (konstanta matematika)"><span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">e</span></a>.</p><p style="margin: 0.5em 0px 1em;">Turunan dengan argumen fungsional rampat <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f</i>(<i>x</i>)</span> dirumuskan sebagai</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\frac {d}{dx}}\ln f(x)={\frac {f'(x)}{f(x)}}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mi>�</mi><mi>�</mi></mrow></mfrac></mrow><mi>ln</mi><mo></mo><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><msup><mi>�</mi><mo>′</mo></msup><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo></mrow><mrow><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo></mrow></mfrac></mrow><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\frac {d}{dx}}\ln f(x)={\frac {f'(x)}{f(x)}}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c06fb9da0538b2a1eefa892ebbfbc3fffdc98bc0" style="border: 0px; display: inline-block; height: 6.509ex; vertical-align: -2.671ex; width: 20.238ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Hasil bagi pada ruas kanan disebut <a href="https://id.wikipedia.org/wiki/Turunan_logaritmik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan logaritmik">turunan logaritmik</a> dari <i><span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">f</span></i> dan menghitung <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f'</i>(<i>x</i>)</span> melalui turunan dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>f</i>(<i>x</i>))</span> dikenal sebagai <a class="new" href="https://id.wikipedia.org/w/index.php?title=Pendiferensialan_logaritmik&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Pendiferensialan logaritmik (halaman belum tersedia)">pendiferensialan logaritmik</a>.<sup class="reference" id="cite_ref-41" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-41" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[38]</a></sup> Antiturunan dari <a href="https://id.wikipedia.org/wiki/Logaritma_alami" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma alami">logaritma alami</a> <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>x</i>)</span> dirumuskan sebagai:<sup class="reference" id="cite_ref-42" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-42" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[39]</a></sup></p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \int \ln(x)\,dx=x\ln(x)-x+C.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>∫</mo><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace><mi>�</mi><mi>�</mi><mo>=</mo><mi>�</mi><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>−</mo><mi>�</mi><mo>+</mo><mi>�</mi><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \int \ln(x)\,dx=x\ln(x)-x+C.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffcaf5c8b14b232de9ff79e9ae0960ea4966bd10" style="border: 0px; display: inline-block; height: 5.676ex; vertical-align: -2.338ex; width: 29.909ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Terdapat <a href="https://id.wikipedia.org/wiki/Daftar_integral_dari_fungsi_logaritmik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Daftar integral dari fungsi logaritmik">rumus yang berkaitan</a>, seperti antiturunan dari logaritma dengan bilangan pokok lainnya dapat diperoleh dari persamaan ini dengan mengubah bilangan pokoknya.<sup class="reference" id="cite_ref-43" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-43" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[40]</a></sup></p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Representasi_integral_mengenai_fungsi_logaritma">Representasi integral mengenai fungsi logaritma</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=17" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Representasi integral mengenai fungsi logaritma">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=17" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Representasi integral mengenai fungsi logaritma">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><figure class="mw-default-size" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Natural_logarithm_integral.svg" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img alt="A hyperbola with part of the area underneath shaded in grey." class="mw-file-element" data-file-height="301" data-file-width="601" decoding="async" height="110" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/df/Natural_logarithm_integral.svg/220px-Natural_logarithm_integral.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Natural_logarithm_integral.svg/330px-Natural_logarithm_integral.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Natural_logarithm_integral.svg/440px-Natural_logarithm_integral.svg.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="220" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;"><a href="https://id.wikipedia.org/wiki/Logaritma_alami" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma alami">Logaritma natural</a> dari <i><span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">t</span></i> adalah luas yang diwarnai di bawah grafik fungsi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f</i>(<i>x</i>) = <span class="sfrac nowrap" style="display: inline-block; font-size: 12.4131px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;">1</span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;"><i>x</i></span></span></span>.</figcaption></figure><p style="margin: 0.5em 0px 1em;"><a href="https://id.wikipedia.org/wiki/Logaritma_alami" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma alami">Logaritma alami</a> dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">t</span> dapat didefinisikan sebagai <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Integral_tentu" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Integral tentu">integral tentu</a>:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \ln t=\int _{1}^{t}{\frac {1}{x}}\,dx.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>ln</mi><mo></mo><mi>�</mi><mo>=</mo><msubsup><mo>∫</mo><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msubsup><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mi>�</mi></mfrac></mrow><mspace width="thinmathspace"></mspace><mi>�</mi><mi>�</mi><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \ln t=\int _{1}^{t}{\frac {1}{x}}\,dx.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab90a884aa3cc91d3cdcfb9b39992598131621e1" style="border: 0px; display: inline-block; height: 6.176ex; vertical-align: -2.338ex; width: 15.687ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Definisi ini menguntungkan karena tidak bergantung pada fungsi eksponensial atau fungsi trigonometri apapun, dan definisi ini merupakan sebuah integral dari fungsi timbal balik sederhana. Penjelasan dalam integral, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>t</i>)</span> sama dengan luas antara sumbu-<span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> dan grafik fungsi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><span class="sfrac nowrap" style="display: inline-block; font-size: 14.042px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;">1</span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;"><i>x</i></span></span></span>, yang berkisar dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>x</i> = 1</span> ke <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>x</i> = <i>t</i></span>. Penjelasan ini juga merupakan akibat dari <a href="https://id.wikipedia.org/wiki/Teorema_dasar_kalkulus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teorema dasar kalkulus">teorema dasar kalkulus</a>, dan bahkan turunan dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>x</i>)</span> sama dengan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><span class="sfrac nowrap" style="display: inline-block; font-size: 14.042px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;">1</span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;"><i>x</i></span></span></span>. Rumus logaritma hasil kali dan pangkat dapat diperoleh melalui definisi ini.<sup class="reference" id="cite_ref-44" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-44" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[41]</a></sup> Sebagai contoh, rumus hasil kali <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>tu</i>) = ln(<i>t</i>) + ln(<i>u</i>)</span> dapat disimpulkan sebagai:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \ln(tu)=\int _{1}^{tu}{\frac {1}{x}}\,dx\ {\stackrel {(1)}{=}}\int _{1}^{t}{\frac {1}{x}}\,dx+\int _{t}^{tu}{\frac {1}{x}}\,dx\ {\stackrel {(2)}{=}}\ln(t)+\int _{1}^{u}{\frac {1}{w}}\,dw=\ln(t)+\ln(u).}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∫</mo><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mi>�</mi></mrow></msubsup><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mi>�</mi></mfrac></mrow><mspace width="thinmathspace"></mspace><mi>�</mi><mi>�</mi><mtext> </mtext><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-REL"><mover><mrow class="MJX-TeXAtom-OP MJX-fixedlimits"><mo>=</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mover></mrow></mrow><msubsup><mo>∫</mo><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msubsup><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mi>�</mi></mfrac></mrow><mspace width="thinmathspace"></mspace><mi>�</mi><mi>�</mi><mo>+</mo><msubsup><mo>∫</mo><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mi>�</mi></mrow></msubsup><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mi>�</mi></mfrac></mrow><mspace width="thinmathspace"></mspace><mi>�</mi><mi>�</mi><mtext> </mtext><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-REL"><mover><mrow class="MJX-TeXAtom-OP MJX-fixedlimits"><mo>=</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mover></mrow></mrow><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>+</mo><msubsup><mo>∫</mo><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msubsup><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mi>�</mi></mfrac></mrow><mspace width="thinmathspace"></mspace><mi>�</mi><mi>�</mi><mo>=</mo><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>+</mo><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \ln(tu)=\int _{1}^{tu}{\frac {1}{x}}\,dx\ {\stackrel {(1)}{=}}\int _{1}^{t}{\frac {1}{x}}\,dx+\int _{t}^{tu}{\frac {1}{x}}\,dx\ {\stackrel {(2)}{=}}\ln(t)+\int _{1}^{u}{\frac {1}{w}}\,dw=\ln(t)+\ln(u).}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1752da5c3291c5b9e267118dc1b96d89c863c458" style="border: 0px; display: inline-block; height: 6.176ex; vertical-align: -2.338ex; width: 79.675ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Persamaan (1) membagi integral menjadi dua bagian, sementara (2) mengubah variabel <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>w</i></span> menjadi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><span class="sfrac nowrap" style="display: inline-block; font-size: 14.042px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;"><i>x</i></span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;"><i>t</i></span></span></span>. Pada ilustrasi dibawah, pembagian integral tersebut dapat disamakan dengan pembagian luasnya menjadi bagian berwarna kuning dan biru. Dengan mengukur luas berwarna biru kembali secara vertikal melalui faktor <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">t</span> dan menyusutnya melalui faktor yang sama secara horizontal tidak mengubah ukuran luasnya. Dengan memindahkan daerah biru ke daerah kuning, luasnya menyesuaikan grafik fungsi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f</i>(<i>x</i>) = <span class="sfrac nowrap" style="display: inline-block; font-size: 14.042px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;">1</span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;"><i>x</i></span></span></span> lagi. Oleh karena itu, luas biru di sebelah kiri, yang merupakan integral dari fungsi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f</i>(<i>x</i>)</span> dengan interval dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">t</span> hingga <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">tu</span> sama dengan integral dari fungsi yang sama dengan interval 1 hingga <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">u</span>. Hal ini membenarkan persamaan (2) melalui bukti geometri lainnya.</p><figure class="mw-halign-center" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: none; display: table; float: none; line-height: 0; margin: 0px auto 0.5em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Natural_logarithm_product_formula_proven_geometrically.svg" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img alt="Fungsi hiperbola digambarkan dua kali. Luas di bawah fungsi dibagi menjadi bagian yang berbeda." class="mw-file-element" data-file-height="304" data-file-width="1353" decoding="async" height="112" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Natural_logarithm_product_formula_proven_geometrically.svg/500px-Natural_logarithm_product_formula_proven_geometrically.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Natural_logarithm_product_formula_proven_geometrically.svg/750px-Natural_logarithm_product_formula_proven_geometrically.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Natural_logarithm_product_formula_proven_geometrically.svg/1000px-Natural_logarithm_product_formula_proven_geometrically.svg.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="500" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Sebuah bukti visual tentang rumus hasil kali dari logaritma natural</figcaption></figure><p style="margin: 0.5em 0px 1em;">Rumus pangkat <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>t</i><sup style="font-size: 13.216px; line-height: 1;"><i>r</i></sup>) = <i>r</i> ln(<i>t</i>)</span> dapat real dalam cara yang serupa:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \ln(t^{r})=\int _{1}^{t^{r}}{\frac {1}{x}}dx=\int _{1}^{t}{\frac {1}{w^{r}}}\left(rw^{r-1}\,dw\right)=r\int _{1}^{t}{\frac {1}{w}}\,dw=r\ln(t).}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∫</mo><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mrow></msubsup><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mi>�</mi></mfrac></mrow><mi>�</mi><mi>�</mi><mo>=</mo><msubsup><mo>∫</mo><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msubsup><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mfrac></mrow><mrow><mo>(</mo><mrow><mi>�</mi><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mo>−</mo><mn>1</mn></mrow></msup><mspace width="thinmathspace"></mspace><mi>�</mi><mi>�</mi></mrow><mo>)</mo></mrow><mo>=</mo><mi>�</mi><msubsup><mo>∫</mo><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msubsup><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mi>�</mi></mfrac></mrow><mspace width="thinmathspace"></mspace><mi>�</mi><mi>�</mi><mo>=</mo><mi>�</mi><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \ln(t^{r})=\int _{1}^{t^{r}}{\frac {1}{x}}dx=\int _{1}^{t}{\frac {1}{w^{r}}}\left(rw^{r-1}\,dw\right)=r\int _{1}^{t}{\frac {1}{w}}\,dw=r\ln(t).}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34505f1f7592f516126015296fdf4889f5235f68" style="border: 0px; display: inline-block; height: 6.343ex; vertical-align: -2.338ex; width: 63.384ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Persamaan kedua menggunakan perubahan variabel <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>w</i> = <span class="texhtml mvar" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">x</span><sup style="font-size: 13.216px; line-height: 1;"><span class="sfrac nowrap" style="display: inline-block; font-size: 11.2336px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;">1</span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;"><i>r</i></span></span></sup></span> melalui <a href="https://id.wikipedia.org/wiki/Integral_substitusi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Integral substitusi">integral substitusi</a>.</p><p style="margin: 0.5em 0px 1em;">Jumlah keseluruhan timbal balik dari bilangan asli yang dirumuskan</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 1+{\frac {1}{2}}+{\frac {1}{3}}+\cdots +{\frac {1}{n}}=\sum _{k=1}^{n}{\frac {1}{k}},}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>1</mn><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow><mo>+</mo><mo>⋯</mo><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mi>�</mi></mfrac></mrow><mo>=</mo><munderover><mo>∑</mo><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mo>=</mo><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></munderover><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mi>�</mi></mfrac></mrow><mo>,</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 1+{\frac {1}{2}}+{\frac {1}{3}}+\cdots +{\frac {1}{n}}=\sum _{k=1}^{n}{\frac {1}{k}},}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12f50a7390e77e5beed851612314d2d03991d564" style="border: 0px; display: inline-block; height: 6.843ex; vertical-align: -3.005ex; width: 31.01ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">disebut <a href="https://id.wikipedia.org/wiki/Deret_harmonik_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Deret harmonik (matematika)">deret harmonik</a>. Deret ini sangat terkait erat dengan <a href="https://id.wikipedia.org/wiki/Logaritma_alami" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma alami">logaritma alami</a>, yang dinyatakan melalui pernyataan berikut: ketika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">n</span> cenderung menuju <a href="https://id.wikipedia.org/wiki/Tak_hingga" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Tak hingga">takhingga</a>, selisih dari</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \sum _{k=1}^{n}{\frac {1}{k}}-\ln(n),}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><munderover><mo>∑</mo><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mo>=</mo><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></munderover><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mi>�</mi></mfrac></mrow><mo>−</mo><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>,</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \sum _{k=1}^{n}{\frac {1}{k}}-\ln(n),}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0f1edf2104b89524c509d6cb9ea1a667251d3ac" style="border: 0px; display: inline-block; height: 6.843ex; vertical-align: -3.005ex; width: 14.42ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;"><a href="https://id.wikipedia.org/wiki/Limit_barisan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Limit barisan">konvergen</a> (yakni mendekati dengan sembarang) ke sebuah bilangan yang dikenal sebagai <a href="https://id.wikipedia.org/wiki/Konstanta_Euler%E2%80%93Mascheroni" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Konstanta Euler–Mascheroni">konstanta Euler–Mascheroni</a> <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>γ</i> = 0,5772...</span>. Kaitan antara deret harmonik dan logaritma natural membantu dalam menganalisis kinerja algoritma seperti <i><a href="https://id.wikipedia.org/wiki/Quicksort" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Quicksort">quicksort</a></i>.<sup class="reference" id="cite_ref-45" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-45" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[42]</a></sup></p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Transendensi_logaritma">Transendensi logaritma</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=18" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Transendensi logaritma">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=18" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Transendensi logaritma">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;">Bilangan real yang bukan merupakan <a href="https://id.wikipedia.org/wiki/Bilangan_aljabar" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan aljabar">bilangan aljabar</a> disebut bilangan transendental<sup class="reference" id="cite_ref-46" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-46" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[43]</a></sup>. Sebagai contoh, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><a href="https://id.wikipedia.org/wiki/Pi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Pi"><i>π</i></a></span> dan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i><a href="https://id.wikipedia.org/wiki/E_(konstanta_matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="E (konstanta matematika)">e</a></i></span> adalah bilangan transendental, sedangkan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\sqrt {2-{\sqrt {3}}}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><msqrt><mn>2</mn><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><msqrt><mn>3</mn></msqrt></mrow></msqrt></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\sqrt {2-{\sqrt {3}}}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75b2a724c326f7f59f71baa9788cf455a0609bdc" style="border: 0px; display: inline-block; height: 4.843ex; margin: 0px; vertical-align: -1.671ex; width: 9.425ex;" /></span> bukan. Hampir semua <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Bilangan_real" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan real">bilangan real</a> adalah <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Bilangan_transendental" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan transendental">transendental</a>. Logaritma merupakan sebuah contoh <a href="https://id.wikipedia.org/wiki/Fungsi_transendental" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi transendental">fungsi transendental</a>. <a href="https://id.wikipedia.org/wiki/Teorema_Gelfond%E2%80%93Schneider" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teorema Gelfond–Schneider">Teorema Gelfond–Schneider</a> mengatakan bahwa logaritma biasanya memberikan nilai transendental.<sup class="reference" id="cite_ref-47" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-47" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[44]</a></sup></p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Perhitungan_2">Perhitungan</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=19" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Perhitungan">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=19" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Perhitungan">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><figure class="mw-default-size" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Logarithm_keys.jpg" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img class="mw-file-element" data-file-height="1411" data-file-width="1882" decoding="async" height="165" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/88/Logarithm_keys.jpg/220px-Logarithm_keys.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Logarithm_keys.jpg/330px-Logarithm_keys.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/88/Logarithm_keys.jpg/440px-Logarithm_keys.jpg 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="220" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Tombol logaritma (LOG sebagai bilangan pokok 10 dan LN sebagai bilangan pokok <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">e</span>) pada sebuah kalkulator grafik <a class="new" href="https://id.wikipedia.org/w/index.php?title=TI-83_series&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="TI-83 series (halaman belum tersedia)">TI-83 Plus</a>.</figcaption></figure><p style="margin: 0.5em 0px 1em;">Logaritma merupakan alat hitung yang mudah pada beberapa kasus, seperti <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;">10</sup>log 1000 = 3</span>. Logaritma pada umumnya dapat dihitung melalui <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Deret_kuasa" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Deret kuasa">deret kuasa</a> atau <a href="https://id.wikipedia.org/wiki/Rata-rata_aritmetika%E2%80%93geometrik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Rata-rata aritmetika–geometrik">rata-rata aritmetika–geometrik</a>, atau didapatkan kembali dari tabel logaritma (sebelum adanya perhitungan logaritma) yang menyediakan ketepatan nilai konstan.<sup class="reference" id="cite_ref-48" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-48" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[45]</a></sup><sup class="reference" id="cite_ref-49" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-49" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[46]</a></sup> <a href="https://id.wikipedia.org/wiki/Metode_Newton" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Metode Newton">Metode Newton</a>, sebuah metode berulang yang menyelesaikan persamaan melalui hampiran, juga dapat dipakai untuk menghitung logaritma, karena fungsi inversnya (yaitu fungsi eksponensial), dapat dihitung dengan cepat.<sup class="reference" id="cite_ref-50" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-50" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[47]</a></sup> Dengan melihat tabel logaritma, metode yang mirip dengan <a href="https://id.wikipedia.org/wiki/CORDIC" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="CORDIC">CORDIC</a> dapat dipakai untuk menghitung logaritma hanya dengan menggunakan operasi penambahan dan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Geseran_aritmetika&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Geseran aritmetika (halaman belum tersedia)">geseran bit</a>.<sup class="reference" id="cite_ref-51" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-51" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[48]</a></sup><sup class="reference" id="cite_ref-52" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-52" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[49]</a></sup> Terlebih lagi, <a href="https://id.wikipedia.org/wiki/Logaritma_biner#Algoritma" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma biner">algoritma dari logaritma biner</a> menghitung <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">lb(<i>x</i>)</span> <a href="https://id.wikipedia.org/wiki/Rekursi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Rekursi">secara berulang</a> berdasarkan penguadratan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> yang berulang dan menggunakan ekspresi</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ^{2}\!\log \left(x^{2}\right)=2\cdot \,^{2}\!\log |x|.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mrow><mo>(</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>)</mo></mrow><mo>=</mo><mn>2</mn><mo>⋅</mo><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ^{2}\!\log \left(x^{2}\right)=2\cdot \,^{2}\!\log |x|.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/554c8616e494d5f8dcc42209ed93c12a4d0c4125" style="border: 0px; display: inline-block; height: 3.343ex; vertical-align: -1.005ex; width: 22.55ex;" /></span></dd></dl><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Deret_pangkat">Deret pangkat</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=20" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Deret pangkat">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=20" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Deret pangkat">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><h4 style="color: black; font-size: 14px; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Deret_Taylor">Deret Taylor</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=21" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Deret Taylor">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=21" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Deret Taylor">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h4><figure class="mw-default-size" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Taylor_approximation_of_natural_logarithm.gif" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img alt="An animation showing increasingly good approximations of the logarithm graph." class="mw-file-element" data-file-height="185" data-file-width="300" decoding="async" height="136" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/02/Taylor_approximation_of_natural_logarithm.gif/220px-Taylor_approximation_of_natural_logarithm.gif" srcset="//upload.wikimedia.org/wikipedia/commons/0/02/Taylor_approximation_of_natural_logarithm.gif 1.5x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="220" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Deret Taylor dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>z</i>)</span> berpusat di <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>z</i> = 1</span>. Animasi berikut memperlihatkan 10 hampiran pertama beserta dengan hampiran yang ke-99 dan yang ke-100. Hampiran tersebut tidak konvergen karena melebihi jarak 1 dari pusatnya.</figcaption></figure><p style="margin: 0.5em 0px 1em;">Untuk setiap bilangan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> yang memenuhi sifat <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">0 < <i>z</i> ≤ 2</span>, maka berlaku rumus:<sup class="reference" id="cite_ref-53" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-53" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[nb 4]</a></sup><sup class="reference" id="cite_ref-AbramowitzStegunp.68_54-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-AbramowitzStegunp.68-54" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[50]</a></sup></p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\begin{aligned}\ln(z)&={\frac {(z-1)^{1}}{1}}-{\frac {(z-1)^{2}}{2}}+{\frac {(z-1)^{3}}{3}}-{\frac {(z-1)^{4}}{4}}+\cdots \\&=\sum _{k=1}^{\infty }(-1)^{k+1}{\frac {(z-1)^{k}}{k}}\end{aligned}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mo stretchy="false">(</mo><mi>�</mi><mo>−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msup></mrow><mn>1</mn></mfrac></mrow><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mo stretchy="false">(</mo><mi>�</mi><mo>−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow><mn>2</mn></mfrac></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mo stretchy="false">(</mo><mi>�</mi><mo>−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup></mrow><mn>3</mn></mfrac></mrow><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mo stretchy="false">(</mo><mi>�</mi><mo>−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>4</mn></mrow></msup></mrow><mn>4</mn></mfrac></mrow><mo>+</mo><mo>⋯</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><munderover><mo>∑</mo><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mo>=</mo><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><mo stretchy="false">(</mo><mo>−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mo>+</mo><mn>1</mn></mrow></msup><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mo stretchy="false">(</mo><mi>�</mi><mo>−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mrow><mi>�</mi></mfrac></mrow></mtd></mtr></mtable></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\begin{aligned}\ln(z)&={\frac {(z-1)^{1}}{1}}-{\frac {(z-1)^{2}}{2}}+{\frac {(z-1)^{3}}{3}}-{\frac {(z-1)^{4}}{4}}+\cdots \\&=\sum _{k=1}^{\infty }(-1)^{k+1}{\frac {(z-1)^{k}}{k}}\end{aligned}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2e5784315dae9de565eb85c06255111aa4cfb49" style="border: 0px; display: inline-block; height: 13.176ex; margin-bottom: -0.24ex; vertical-align: -5.765ex; width: 57.934ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Pernyataan di atas merupakan tulisan singkat untuk mengatakan bahwa <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>z</i>)</span> dapat diaproksimasi sebagai bilangan yang lebih-lebih akurat lagi melalui ekspresi berikut:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\begin{array}{lllll}(z-1)&&\\(z-1)&-&{\frac {(z-1)^{2}}{2}}&\\(z-1)&-&{\frac {(z-1)^{2}}{2}}&+&{\frac {(z-1)^{3}}{3}}\\\vdots &\end{array}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mtable columnalign="left left left left left" columnspacing="1em" rowspacing="4pt"><mtr><mtd><mo stretchy="false">(</mo><mi>�</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo></mtd><mtd></mtd><mtd></mtd></mtr><mtr><mtd><mo stretchy="false">(</mo><mi>�</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo></mtd><mtd><mo>−</mo></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mo stretchy="false">(</mo><mi>�</mi><mo>−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow><mn>2</mn></mfrac></mrow></mtd><mtd></mtd></mtr><mtr><mtd><mo stretchy="false">(</mo><mi>�</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo></mtd><mtd><mo>−</mo></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mo stretchy="false">(</mo><mi>�</mi><mo>−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow><mn>2</mn></mfrac></mrow></mtd><mtd><mo>+</mo></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mo stretchy="false">(</mo><mi>�</mi><mo>−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup></mrow><mn>3</mn></mfrac></mrow></mtd></mtr><mtr><mtd><mo>⋮</mo></mtd><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\begin{array}{lllll}(z-1)&&\\(z-1)&-&{\frac {(z-1)^{2}}{2}}&\\(z-1)&-&{\frac {(z-1)^{2}}{2}}&+&{\frac {(z-1)^{3}}{3}}\\\vdots &\end{array}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ee42affec068dac4ef60dc45a26bf227eb66d07" style="border: 0px; display: inline-block; height: 17.176ex; vertical-align: -8.005ex; width: 32.192ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Sebagai contoh, pendekatan ketiga saat <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>z</i> = 1,5</span> memberikan nilai 0,4167. Nilai tersebut kira-kira 0,011 lebih besar dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(1,5) = 0,405465</span>. <a href="https://id.wikipedia.org/wiki/Deret_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Deret (matematika)">Deret</a> ini yang mengaproksimasi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>z</i>)</span> dengan ketepatan nilai sembarang, menyediakan jumlah dari nilai yang dijumlahkan cukup besar. Dalam kalkulus elementer, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>z</i>)</span> adalah <a class="mw-disambig" href="https://id.wikipedia.org/wiki/Limit" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Limit">limit</a> dari deret ini dan juga merupakan <a href="https://id.wikipedia.org/wiki/Deret_Taylor" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Deret Taylor">deret Taylor</a> dari <a href="https://id.wikipedia.org/wiki/Logaritma_alami" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma alami">logaritma alami</a> di <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>z</i> = 1</span>. Deret Taylor dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>z</i>)</span> khususnya menyediakan alat yang berguna untuk mengaproksimasi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(1 + <i>z</i>)</span> ketika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> bernilai kecil, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">|<i>z</i>| < 1</span>:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \ln(1+z)=z-{\frac {z^{2}}{2}}+{\frac {z^{3}}{3}}\cdots \approx z.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><mi>�</mi><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mn>2</mn></mfrac></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup><mn>3</mn></mfrac></mrow><mo>⋯</mo><mo>≈</mo><mi>�</mi><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \ln(1+z)=z-{\frac {z^{2}}{2}}+{\frac {z^{3}}{3}}\cdots \approx z.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e89327f36f52ef490f4bf487c232afc707e4bfb" style="border: 0px; display: inline-block; height: 5.676ex; vertical-align: -1.838ex; width: 32.612ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Sebagai contoh, hampiran orde pertama memberikan nilai hampiran <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(1,1) ≈ 0,1</span> ketika <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>z</i> = 0,1</span>, yang galatnya 5% lebih kecil dari nilai eksak 0,0953.</p><h4 style="color: black; font-size: 14px; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Deret_lebih_efisien">Deret lebih efisien</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=22" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Deret lebih efisien">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=22" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Deret lebih efisien">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h4><p style="margin: 0.5em 0px 1em;">Deret lainnya berasal dari <a href="https://id.wikipedia.org/wiki/Fungsi_hiperbolik_invers#Fungsi_tangen_hiperbolik_invers" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi hiperbolik invers">fungsi tangen hiperbolik invers</a>:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \ln(z)=2\cdot \operatorname {artanh} \,{\frac {z-1}{z+1}}=2\left({\frac {z-1}{z+1}}+{\frac {1}{3}}{\left({\frac {z-1}{z+1}}\right)}^{3}+{\frac {1}{5}}{\left({\frac {z-1}{z+1}}\right)}^{5}+\cdots \right),}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><mn>2</mn><mo>⋅</mo><mi>artanh</mi><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi>�</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow><mo>=</mo><mn>2</mn><mrow><mo>(</mo><mrow><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi>�</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow><msup><mrow class="MJX-TeXAtom-ORD"><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi>�</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mn>5</mn></mfrac></mrow><msup><mrow class="MJX-TeXAtom-ORD"><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi>�</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mrow class="MJX-TeXAtom-ORD"><mn>5</mn></mrow></msup><mo>+</mo><mo>⋯</mo></mrow><mo>)</mo></mrow><mo>,</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \ln(z)=2\cdot \operatorname {artanh} \,{\frac {z-1}{z+1}}=2\left({\frac {z-1}{z+1}}+{\frac {1}{3}}{\left({\frac {z-1}{z+1}}\right)}^{3}+{\frac {1}{5}}{\left({\frac {z-1}{z+1}}\right)}^{5}+\cdots \right),}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e4774ed055db87556b991ffc8dcf5bd795f823c" style="border: 0px; display: inline-block; height: 7.509ex; vertical-align: -3.171ex; width: 75.541ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">untuk setiap bilangan real <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>z</i> > 0</span>.<sup class="reference" id="cite_ref-55" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-55" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[nb 5]</a></sup><sup class="reference" id="cite_ref-AbramowitzStegunp.68_54-1" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-AbramowitzStegunp.68-54" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[50]</a></sup> Dengan menggunakan <a href="https://id.wikipedia.org/wiki/Notasi_Sigma" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Notasi Sigma">notasi Sigma</a>, ruas kanan pada rumus di atas juga dapat ditulis sebagai</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \ln(z)=2\sum _{k=0}^{\infty }{\frac {1}{2k+1}}\left({\frac {z-1}{z+1}}\right)^{2k+1}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><mn>2</mn><munderover><mo>∑</mo><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mo>=</mo><mn>0</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mrow><mn>2</mn><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow><msup><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi>�</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mn>2</mn><mi>�</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \ln(z)=2\sum _{k=0}^{\infty }{\frac {1}{2k+1}}\left({\frac {z-1}{z+1}}\right)^{2k+1}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d9729501b26eb85764942cb112cc9885b1a6cca" style="border: 0px; display: inline-block; height: 7.343ex; vertical-align: -3.171ex; width: 34.446ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Deret ini dapat diturunkan dari deret Taylor di atas, yang konvergen lebih cepat daripada deret Taylor, khususnya jika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> mendekati 1. Sebagai contoh, untuk <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>z</i> = 1,5</span>, tiga suku pertama dari deret kedua memberikan nilai hampiran <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(1,5)</span> dengan galatnya sekitar <span class="nowrap" style="text-wrap: nowrap;"><span data-sort-value="6994300000000000000♠"></span>3<span style="margin-left: 0.25em; margin-right: 0.15em;">×</span>10<sup style="font-size: 11.2px; line-height: 1;">−6</sup></span>. Kekonvergenan cepat untuk <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> yang mendekati 1 dapat dimanfaatkan sebagai berikut: diberikan sebuah hampiran dengan tingkat akurat yang rendah <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>y</i> ≈ ln(<i>z</i>)</span> dan memasukkan ke rumus</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle A={\frac {z}{\exp(y)}},}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mi>exp</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo></mrow></mfrac></mrow><mo>,</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle A={\frac {z}{\exp(y)}},}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70dc2d5fb51bc065e7662ba91fe25996896dfa2e" style="border: 0px; display: inline-block; height: 5.509ex; vertical-align: -2.671ex; width: 12.842ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">maka logaritma dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> dirumuskan:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \ln(z)=y+\ln(A).}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><mi>�</mi><mo>+</mo><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \ln(z)=y+\ln(A).}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ea935537fad8ed9632a4e0eaa453c172906606c" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.838ex; width: 18.07ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Hampiran awalan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> yang lebih baik adalah dengan membuat nilai <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">A</span> mendekati ke 1, sehingga nilai logaritma dapat dihitung lebih efisien. Nilai <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">A</span> dapat dihitung melalui <a href="https://id.wikipedia.org/wiki/Fungsi_eksponensial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi eksponensial">deret eksponensial</a> sehingga nilainya konvergen dengan cepat, asalkan nilai <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> tidak terlalu besar. Dengan menghitung logaritma dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> yang lebih besar dapat direduksi menjadi nilai <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> yang lebih kecil dengan menulis <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>z</i> = <i>a</i> · 10<sup style="font-size: 13.216px; line-height: 1;"><i>b</i></sup></span>, sehingga <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>z</i>) = ln(<i>a</i>) + <span class="texhtml mvar" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">b</span> · ln(10)</span>.</p><p style="margin: 0.5em 0px 1em;">Terdapat metode yang sangat berkaitan dengannya dapat dipakai untuk menghitung logaritma dari bilangan bulat. Dengan memasukkan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \textstyle z={\frac {n+1}{n}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="false" scriptlevel="0"><mi>�</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow><mi>�</mi></mfrac></mrow></mstyle></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \textstyle z={\frac {n+1}{n}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4197236e535dc6467df2570a52e72ec095f7fd2" style="border: 0px; display: inline-block; height: 3.509ex; margin: 0px; vertical-align: -1.005ex; width: 8.109ex;" /></span> pada deret di atas, maka deret tersebut dapat ditulis sebagai berikut:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \ln(n+1)=\ln(n)+2\sum _{k=0}^{\infty }{\frac {1}{2k+1}}\left({\frac {1}{2n+1}}\right)^{2k+1}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mo>=</mo><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>+</mo><mn>2</mn><munderover><mo>∑</mo><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mo>=</mo><mn>0</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mrow><mn>2</mn><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow><msup><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mrow><mn>2</mn><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mn>2</mn><mi>�</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \ln(n+1)=\ln(n)+2\sum _{k=0}^{\infty }{\frac {1}{2k+1}}\left({\frac {1}{2n+1}}\right)^{2k+1}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/306cedcb8ef32fe57d535b3c27b2ae6af9b13326" style="border: 0px; display: inline-block; height: 7.343ex; vertical-align: -3.171ex; width: 48.208ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Jika diketahui logaritma dari suatu bilangan bulat <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">n</span> yang lebih besar, maka deret tersebut menghasilkan sebauah deret yang konvergen dengan cepat untuk <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log(<i>n</i>+1)</span>, dengan <a href="https://id.wikipedia.org/wiki/Laju_konvergensi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Laju konvergensi">laju konvergensi</a> dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\textstyle \left({\frac {1}{2n+1}}\right)^{2}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><msup><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mrow><mn>2</mn><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\textstyle \left({\frac {1}{2n+1}}\right)^{2}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6c094c1c61f349b1216928c33fe29aa61860626" style="border: 0px; display: inline-block; height: 5.176ex; margin: 0px; vertical-align: -1.838ex; width: 8.575ex;" /></span>.</p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Hampiran_purata_aritmetika-geometrik">Hampiran purata aritmetika-geometrik</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=23" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Hampiran purata aritmetika-geometrik">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=23" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Hampiran purata aritmetika-geometrik">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;"><a class="mw-redirect" href="https://id.wikipedia.org/wiki/Purata_aritmetika%E2%80%93geometrik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Purata aritmetika–geometrik">Purata aritmetika–geometrik</a> atau <a href="https://id.wikipedia.org/wiki/Rata-rata_aritmetika%E2%80%93geometrik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Rata-rata aritmetika–geometrik">rata-rata aritmetika–geometrik</a> menghasilkan hampiran dari <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Logaritma_natural" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma natural">logaritma natural</a> dengan tingkatan ketepatan yang tinggi. Pada tahun 1982, Sasaki dan Kanada memperlihatkan bahwa purata ini sangat cepat untuk ketepatan di antara 400 dan 1000 letak desimal, sementara metode deret Taylor biasanya lebih cepat ketika membutuhkan nilai yang kurang akurat. Dalam karyanya, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>x</i>)</span> kira-kira sama dengan ketepatan dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">2<sup style="font-size: 13.216px; line-height: 1;">−<i>p</i></sup></span> (atau <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">p</span> bit yang tepat) melalui rumus berikut (karena <a href="https://id.wikipedia.org/wiki/Carl_Friedrich_Gauss" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Carl Friedrich Gauss">Carl Friedrich Gauss</a>):<sup class="reference" id="cite_ref-56" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-56" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[51]</a></sup><sup class="reference" id="cite_ref-57" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-57" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[52]</a></sup></p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \ln(x)\approx {\frac {\pi }{2\,\mathrm {M} \!\left(1,2^{2-m}/x\right)}}-m\ln(2).}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>≈</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mn>2</mn><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">M</mi></mrow><mspace width="negativethinmathspace"></mspace><mrow><mo>(</mo><mrow><mn>1</mn><mo>,</mo><msup><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mn>2</mn><mo>−</mo><mi>�</mi></mrow></msup><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>�</mi></mrow><mo>)</mo></mrow></mrow></mfrac></mrow><mo>−</mo><mi>�</mi><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \ln(x)\approx {\frac {\pi }{2\,\mathrm {M} \!\left(1,2^{2-m}/x\right)}}-m\ln(2).}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec803ea11552f9cdfd17caf1b39cf8e7a8e84184" style="border: 0px; display: inline-block; height: 6.009ex; vertical-align: -3.171ex; width: 35.276ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Notasi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">M(<i>x</i>, <i>y</i>)</span> menyatakan <a href="https://id.wikipedia.org/wiki/Rata-rata_aritmetika%E2%80%93geometrik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Rata-rata aritmetika–geometrik">rata-rata aritmetika–geometrik</a> dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> dan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span>. Purata ini didapatkan dengan menghitung rerata <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">(<i>x</i> + <i>y</i>)/2</span> (<a class="mw-redirect" href="https://id.wikipedia.org/wiki/Purata_aritmetika" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Purata aritmetika">purata aritmetika</a>) dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\textstyle {\sqrt {xy}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><msqrt><mi>�</mi><mi>�</mi></msqrt></mrow></mstyle></mrow></semantics></math></span><img alt="{\textstyle {\sqrt {xy}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/966df76a5bc207e11606ad5c8ea6788d6a838c47" style="border: 0px; display: inline-block; height: 3.009ex; margin: 0px; vertical-align: -1.171ex; width: 4.421ex;" /></span> (<a class="mw-redirect" href="https://id.wikipedia.org/wiki/Purata_geometrik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Purata geometrik">purata geometrik</a>) dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> dan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> secara berulang, lalu misalkan kedua bilangan tersebut merupakan bilangan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> dan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> selanjutnya. Kedua bilangan tersebut konvergen dengan cepat menuju ke limit yang sama, yaitu <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">M(<i>x</i>, <i>y</i>)</span>. Agar pasti bahwa nilai yang diperlukan tepat, maka pilih <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">m</span> sehingga</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x\,2^{m}>2^{p/2}.\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mspace width="thinmathspace"></mspace><msup><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>></mo><msup><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup><mo>.</mo><mspace width="thinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x\,2^{m}>2^{p/2}.\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80443424cc40c061dba53d32f86d2d8169aa1983" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.338ex; width: 12.552ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Bilangan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">m</span> yang lebih besar membuat perhitungan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">M(<i>x</i>, <i>y</i>)</span>, dengan nilai awal <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> dan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> yang merupakan nilai yang sangat jauh, mengambil langkah lebih lanjut agar nilainya konvergen, tetapi memberikan nilai yang lebih tepat. Konstanta seperti <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">π</span> dan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(2)</span> dapat dihitung melalui deret yang konvergen dengan cepat.</p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Algoritma_Feynman">Algoritma Feynman</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=24" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Algoritma Feynman">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=24" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Algoritma Feynman">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;"><a href="https://id.wikipedia.org/wiki/Richard_Feynman" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Richard Feynman">Richard Feynman</a>, yang mengerjakan <a href="https://id.wikipedia.org/wiki/Proyek_Manhattan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Proyek Manhattan">proyek Manhattan</a> di <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Los_Alamos_National_Laboratory" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Los Alamos National Laboratory">Los Alamos National Laboratory</a>, mengembangkan sebuah algoritma pengolahan bit untuk menghitung nilai logaritma. Algoritma tersebut menyerupai pembagian panjang, dan kemudian dipakai dalam sebuah anggota dari rangkaian subkomputer, <a href="https://id.wikipedia.org/wiki/Connection_Machine" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Connection Machine">Connection Machine</a>. Bahkan bahwa setiap bilangan real <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">1 < <i>x</i> < 2</span> yang dapat direpresentasikan sebagai hasil kali dari faktor yang berbeda dari bentuk <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">1 + 2<sup style="font-size: 13.216px; line-height: 1;">−<i>k</i></sup></span>, dipakai dalam algoritma ini. Algoritma ini dibangun secara berurutan bahwa hasil kali <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">P</span>, yang dimulai dengan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>P</i> = 1</span> dan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>k</i> = 1</span>, mengatakan bahwa jika <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>P</i> · (1 + 2<sup style="font-size: 13.216px; line-height: 1;">−<i>k</i></sup>) < <i>x</i></span>, maka <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">P</span> berubah menjadi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>P</i> · (1 + 2<sup style="font-size: 13.216px; line-height: 1;">−<i>k</i></sup>)</span>, sehingga membuat nilai <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle k}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle k}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 1.211ex;" /></span> menaik. Algoritma tersebut berhenti ketika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">k</span> cukup besar memberikan nilai akurat yang diinginkan. Karena <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log(<i>x</i>)</span> adalah jumlah dari suku berbentuk <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log(1 + 2<sup style="font-size: 13.216px; line-height: 1;">−<i>k</i></sup>)</span> yang berpadanan dengan nilai <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">k</span> dan faktor <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">1 + 2<sup style="font-size: 13.216px; line-height: 1;">−<i>k</i></sup></span> adalah hasil kali dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">P</span>, maka <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log(<i>x</i>)</span> dapat dihitung melalui operasi penambahan yang sederhana, yaitu menggunakan tabel dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log(1 + 2<sup style="font-size: 13.216px; line-height: 1;">−<i>k</i></sup>)</span> untuk semua <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">k</span>. Setiap bilangan pokok dapat dipakai untuk tabel logaritma.<sup class="reference" id="cite_ref-58" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-58" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[53]</a></sup></p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Penerapan">Penerapan</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=25" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Penerapan">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=25" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Penerapan">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><figure class="mw-default-size" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:NautilusCutawayLogarithmicSpiral.jpg" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img alt="A photograph of a nautilus' shell." class="mw-file-element" data-file-height="1693" data-file-width="2240" decoding="async" height="166" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/08/NautilusCutawayLogarithmicSpiral.jpg/220px-NautilusCutawayLogarithmicSpiral.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/NautilusCutawayLogarithmicSpiral.jpg/330px-NautilusCutawayLogarithmicSpiral.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/08/NautilusCutawayLogarithmicSpiral.jpg/440px-NautilusCutawayLogarithmicSpiral.jpg 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="220" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Sebuah cangkang <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Nautilus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Nautilus">nautilus</a> yang menampilkan bentuk spiral logaritmik.</figcaption></figure><p style="margin: 0.5em 0px 1em;">Logaritma memiliki banyak penerapan di dalam maupun di luar matematika. Ada beberapa kejadian penerapan logaritma yang berkaitan dengan gagasan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Kekararan_skala&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Kekararan skala (halaman belum tersedia)">kekararan skala</a>. Sebagai contoh, setiap ruangan yang terdapat di dalam sebuah cangkang <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Nautilus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Nautilus">nautilus</a> memiliki kira-kira sama dengan jumlah salinan dari ruang selanjutnya, yang ditimbang melalui faktor konstanta. Contoh tersebut menyerupai bentuk <a href="https://id.wikipedia.org/wiki/Spiral_logaritmik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Spiral logaritmik">spiral logaritmik</a>.<sup class="reference" id="cite_ref-59" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-59" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[54]</a></sup> <a href="https://id.wikipedia.org/wiki/Hukum_Benford" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Hukum Benford">Hukum Benford</a> mengenai distribusi dari angka yang ditunjuk juga dapat dijelaskan melalui kekeraran skala.<sup class="reference" id="cite_ref-60" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-60" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[55]</a></sup> Logaritma juga berkaitan dengan benda yang memiliki <a href="https://id.wikipedia.org/wiki/Kemiripan_diri_sendiri" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kemiripan diri sendiri">kemiripan terhadap diri sendiri</a>. Sebagai contoh, logaritma muncul dalam analisis tentang algoritma yang menyelesaikan masalah dengan membaginya menjadi dua masalah lebih kecil yang serupa dan memotong kecil penyelesaiannya.<sup class="reference" id="cite_ref-61" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-61" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[56]</a></sup> Dimensi dari bentuk geometrik menyerupai diri sendiri, dalam artian bahwa bentuk yang bagiannya menyerupai gambarnya secara keseluruhan juga dirumuskan melalui logaritma. <a href="https://id.wikipedia.org/wiki/Skala_logaritmik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Skala logaritmik">Skala logaritmik</a> berguna untuk mengukur perubahan relatif nilai daripada selisih mutlaknya. Terlebih lagi, karena fungsi logaritmik <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log(<i>x</i>)</span> menaik sangat lambat untuk nilai besar<span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>, skala logaritmik biasanya menekan data ilmiah yang berskala besar. Logaritma juga muncul dalam rumus ilmiah numerik, seperti <a href="https://id.wikipedia.org/wiki/Persamaan_roket_Tsiolkovsky" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Persamaan roket Tsiolkovsky">persamaan roket Tsiolkovsky</a>, <a href="https://id.wikipedia.org/wiki/Persamaan_Fenske" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Persamaan Fenske">persamaan Fenske</a>, atau <a href="https://id.wikipedia.org/wiki/Persamaan_Nernst" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Persamaan Nernst">persamaan Nernst</a>.</p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Penerapannya_dalam_skala_logaritmik">Penerapannya dalam skala logaritmik</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=26" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Penerapannya dalam skala logaritmik">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=26" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Penerapannya dalam skala logaritmik">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><div class="hatnote navigation-not-searchable" role="note" style="font-style: italic; margin-bottom: 0.5em; padding-left: 1.6em;">Artikel utama: <a href="https://id.wikipedia.org/wiki/Skala_logaritmik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Skala logaritmik">Skala logaritmik</a></div><figure class="mw-default-size mw-halign-left" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: left; display: table; float: left; line-height: 0; margin: 0.5em 1.4em 1.3em 0px; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Germany_Hyperinflation.svg" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img alt="Grafik yang menggambarkan nilai dari waktu ke waktu. Melalui skala logaritma, garis pada grafik memperlihatkan nilainya yang menaik dengan cepat." class="mw-file-element" data-file-height="594" data-file-width="509" decoding="async" height="257" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Germany_Hyperinflation.svg/220px-Germany_Hyperinflation.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Germany_Hyperinflation.svg/330px-Germany_Hyperinflation.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Germany_Hyperinflation.svg/440px-Germany_Hyperinflation.svg.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="220" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Grafik logaritma memperlihatkan kenaikan harga mata uang <a href="https://id.wikipedia.org/wiki/Mark_Jerman" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Mark Jerman"><i>goldmark</i></a> di <a href="https://id.wikipedia.org/wiki/Papiermark_Jerman" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Papiermark Jerman">Papiermark</a> selama berlangsungnya <a href="https://id.wikipedia.org/wiki/Inflasi_di_Republik_Weimar" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Inflasi di Republik Weimar">hiperinflasi di Jerman pada tahun 1920-an</a></figcaption></figure><p style="margin: 0.5em 0px 1em;">Satuan kuantitas dalam ilmiah seringkali dinyatakan sebagai logaritma dari kuantitas lain, dengan menggunakan <i>skala logaritmik</i>. Sebagai contoh, <a href="https://id.wikipedia.org/wiki/Desibel" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Desibel">desibel</a> merupakan <a href="https://id.wikipedia.org/wiki/Satuan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Satuan">satuan pengukuran</a> yang dikaitkan dengan perhitungan dari <a class="new" href="https://id.wikipedia.org/w/index.php?title=Tingkatan_(kuantitas_logaritma)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Tingkatan (kuantitas logaritma) (halaman belum tersedia)">kuantitas</a> <a href="https://id.wikipedia.org/wiki/Skala_logaritmik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Skala logaritmik">skala logaritmik</a>. Penguat desibel memberikan 10 kalinya logaritma biasa dari <a class="mw-redirect mw-disambig" href="https://id.wikipedia.org/wiki/Rasio" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Rasio">rasio</a> <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Daya_(fisika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Daya (fisika)">daya</a> atau 20 kalinya logaritma biasa dari rasio <a href="https://id.wikipedia.org/wiki/Tegangan_listrik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Tegangan listrik">tegangan</a>. Satuan inilah yang dipakai untuk mengukur rugi tingkatan ketegangan saat mentransmisi sinyal elektrik,<sup class="reference" id="cite_ref-62" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-62" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[57]</a></sup> yang bertujuan untuk menjelaskan tingkatan kekuatan aras daya suara dalam <a class="mw-disambig" href="https://id.wikipedia.org/wiki/Akustik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Akustik">akustik</a>,<sup class="reference" id="cite_ref-63" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-63" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[58]</a></sup> serta mengukur <a href="https://id.wikipedia.org/wiki/Absorbansi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Absorbansi">penyerapan</a> cahaya dalam bidang <a href="https://id.wikipedia.org/wiki/Spektrometer" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Spektrometer">spektrometri</a> dan <a href="https://id.wikipedia.org/wiki/Optika" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Optika">optika</a>. Selain itu, desibel juga dipakai dalam <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Nisbah_sinyal-derau" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Nisbah sinyal-derau">nisbah sinyal-derau</a> yang menjelaskan seberapa banyak <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Derau_(elektronik)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Derau (elektronik)">derau</a> dibandingkan dengan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Sinyal_(elektrik)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Sinyal (elektrik)">sinyal</a> yang berguna.<sup class="reference" id="cite_ref-64" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-64" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[59]</a></sup> Mirip dengan tadi, <a href="https://id.wikipedia.org/wiki/Nisbah_puncak_sinyal_terhadap_derau" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Nisbah puncak sinyal terhadap derau">nisbah puncak sinyal-derau</a> biasanya dipakai menilai kualitas suara dan metode <a href="https://id.wikipedia.org/wiki/Pemampatan_citra" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Pemampatan citra">pemampatan citra</a> melalui logaritma.<sup class="reference" id="cite_ref-65" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-65" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[60]</a></sup></p><p style="margin: 0.5em 0px 1em;">Kekuatan gempa bumi diukur dengan mengambil logaritma umum dari energi yang dipancarkan saat terjadinya gempa dalam satuan <a href="https://id.wikipedia.org/wiki/Skala_magnitudo_momen" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Skala magnitudo momen">skala magnitudo momen</a> atau <a href="https://id.wikipedia.org/wiki/Skala_Richter" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Skala Richter">skala magnitudo Ritcher</a>. Sebagai contoh, gempa berkekuatan 5,0 melepaskan 32 kali <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">(10<sup style="font-size: 13.216px; line-height: 1;">1,5</sup>)</span> dan gempa berkekuatan 6,0 melepaskan 1000 kali<span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">(10<sup style="font-size: 13.216px; line-height: 1;">3</sup>)</span> energi berkekuatan 4,0.<sup class="reference" id="cite_ref-66" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-66" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[61]</a></sup> Skala logaritmik juga dipakai dalam <a href="https://id.wikipedia.org/wiki/Magnitudo_semu" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Magnitudo semu">magnitudo kentara</a> untuk mengukur kecerahan bintang.<sup class="reference" id="cite_ref-67" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-67" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[62]</a></sup> Dalam <a href="https://id.wikipedia.org/wiki/Kimia" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kimia">kimia</a>, negatif dari logaritma desimal, yang disebut sebagai <b>kologaritma</b> desimal, ditunjukkan dengan huruf "p".<sup class="reference" id="cite_ref-Jens_68-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-Jens-68" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[63]</a></sup> Sebagai contoh, <a href="https://id.wikipedia.org/wiki/PH" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="PH">pH</a> merupakan kologaritma desimal dari <a href="https://id.wikipedia.org/wiki/Aktivitas_termodinamika" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Aktivitas termodinamika">keaktifan</a> dari <a href="https://id.wikipedia.org/wiki/Ion" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Ion">ion</a> berbentuk <a href="https://id.wikipedia.org/wiki/Hidrogen" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Hidrogen">hidrogen</a> <span class="chemf nowrap" style="text-wrap: nowrap;">H<sup style="font-size: 11.2px; line-height: 1;">+</sup></span> yang terbentuk dari air, <a href="https://id.wikipedia.org/wiki/Hidronium" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Hidronium">hidronium</a>.<sup class="reference" id="cite_ref-69" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-69" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[64]</a></sup> Keaktifan dari ion hidronium dalam air yang netral bernilai 10<sup style="font-size: 11.2px; line-height: 1;">−7</sup> <a href="https://id.wikipedia.org/wiki/Molaritas" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Molaritas">mol·L<sup style="font-size: 11.2px; line-height: 1;">−1</sup></a>, sehingga nilai pH adalah 7. Contoh lainnya, nilai pH dari asam cuka biasanya sekitar 3. Perbedaan nilai sebesar 4 sesuai dengan rasio 10<sup style="font-size: 11.2px; line-height: 1;">4</sup> berdasarkan aktivitasnya, yaitu nilai dari aktivitas ion hidronium cuka sekitar 10<sup style="font-size: 11.2px; line-height: 1;">−3</sup> mol·L<sup style="font-size: 11.2px; line-height: 1;">−1</sup>.</p><p style="margin: 0.5em 0px 1em;">Konsep skala logaritmik dapat dipakai dalam grafik (log-linear) <a class="new" href="https://id.wikipedia.org/w/index.php?title=Plot_semilog&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Plot semilog (halaman belum tersedia)">semilog</a> bertujuan untuk memberikan visual terkait satu sumbu, yang biasanya berupa sumbu vertikal, diukur menggunakan perhitungan logaritma. Contohnya seperti grafik disamping menjelaskan nilai yang menaik dengan tajam dari 1 juta hingga 1 triliun ke dalam ruang yang sama (pada sumbu vertikal) saat grafiknya menaik dari 1 hingga 1 juta. Pada grafik tersebut, <a href="https://id.wikipedia.org/wiki/Fungsi_eksponensial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi eksponensial">fungsi eksponensial</a> <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f</i>(<i>x</i>) = <i>a</i> · <i>b</i><span style="padding-left: 0.12em;"><sup style="font-size: 13.216px; line-height: 1;"><i>x</i></sup></span></span> muncul sebagai garis lurus dengan <a href="https://id.wikipedia.org/wiki/Kemiringan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kemiringan">kemiringan</a> yang sama dengan logaritma dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span>. Selain itu, skala logaritma yang dapat dipakai dalam <a class="new" href="https://id.wikipedia.org/w/index.php?title=Grafik_log-log&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Grafik log-log (halaman belum tersedia)">grafik log-log</a> untuk mengukur sumbu vertikal dan horizontal, sehingga menyebabkan fungsi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f</i>(<i>x</i>) = <i>a</i> · <i>x</i><span style="padding-left: 0.12em;"><sup style="font-size: 13.216px; line-height: 1;"><i>k</i></sup></span></span> digambarkan sebagai garis lurus yang mempunyai kemiringan yang sama dengan bilangan yang dipangkat dengan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">k</span>, diterapkan pada saat memberikan visual dan menganalisis <a class="new" href="https://id.wikipedia.org/w/index.php?title=Hukum_pangkat&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Hukum pangkat (halaman belum tersedia)">hukum pangkat</a>.<sup class="reference" id="cite_ref-70" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-70" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[65]</a></sup></p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Penerapannya_dalam_psikologi">Penerapannya dalam psikologi</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=27" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Penerapannya dalam psikologi">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=27" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Penerapannya dalam psikologi">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;">Penerapan logaritma juga terdapat dalam beberapa hukum yang menjelaskan tentang <a href="https://id.wikipedia.org/wiki/Persepsi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Persepsi">persepsi manusia</a>.<sup class="reference" id="cite_ref-71" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-71" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[66]</a></sup><sup class="reference" id="cite_ref-72" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-72" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[67]</a></sup> Sebagai contoh, <a href="https://id.wikipedia.org/wiki/Hukum_Hick" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Hukum Hick">hukum Hick</a> menjelaskan kaitan logaritmik antara waktu saat orang mengambil keputusan beserta jumlah keputusan yang dimiliki.<sup class="reference" id="cite_ref-73" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-73" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[68]</a></sup> Hukum lainnya adalah <a href="https://id.wikipedia.org/wiki/Hukum_Fitts" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Hukum Fitts">hukum Fitts</a>, yang memprediksi bahwa waktu yang diperlukan saat bergerak ke daerah target dengan cepat sama dengan fungsi logaritmik dari jarak dan ukuran target.<sup class="reference" id="cite_ref-74" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-74" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[69]</a></sup> Dalam <a href="https://id.wikipedia.org/wiki/Psikofisika" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Psikofisika">psikofisika</a>, <a href="https://id.wikipedia.org/wiki/Hukum_Weber%E2%80%93Fechner" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Hukum Weber–Fechner">hukum Weber–Fechner</a> mengatakan kaitan logaritmik dengan <a href="https://id.wikipedia.org/wiki/Stimulus_(psikologi)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Stimulus (psikologi)">stimulus</a> dan <a href="https://id.wikipedia.org/wiki/Indra_(fisiologi)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Indra (fisiologi)">sensasi</a> yang dirasakan, contohnya seperti saat orang sedang membawa berat benda yang sesungguhnya dengan yang dirasakan.<sup class="reference" id="cite_ref-75" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-75" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[70]</a></sup> (Namun, "hukum" ini kurang realistis dengan model belakangan ini, seperti <a href="https://id.wikipedia.org/wiki/Hukum_perpangkatan_Stevens" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Hukum perpangkatan Stevens">hukum perpangkatan Stevens</a>.<sup class="reference" id="cite_ref-76" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-76" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[71]</a></sup>)</p><p style="margin: 0.5em 0px 1em;">Studi psikologi menemukan bahwa orang yang sedikit mempunyai pemahaman matematika cenderung mengestimasi nilai kuantitas dengan logaritma, atau dengan kata lain, bilangannya ditempatkan pada garis yang tidak ditandai berdasarkan perhitungan logaritma, sehingga 10 yang ditempatkan mendekati 100 dianggap sebagai 100 yang ditempatkan mendekati 1000. Orang yang memiliki pemahaman yang lebih tinggi memandang hal tersebut sebagai linear yang mengestimasi (letak angka 1000 yang berjarak 10 kali lebih jauh) pada beberapa kasus, namun logaritma dipakai pada saat memplot bilangan-bilangan yang sulit untuk diplotkan secara linear.<sup class="reference" id="cite_ref-77" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-77" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[72]</a></sup><sup class="reference" id="cite_ref-78" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-78" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[73]</a></sup></p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Penerapannya_dalam_teori_peluang_dan_statistika">Penerapannya dalam teori peluang dan statistika</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=28" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Penerapannya dalam teori peluang dan statistika">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=28" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Penerapannya dalam teori peluang dan statistika">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><div class="thumb tmulti tright" style="background-color: transparent; clear: right; float: right; margin: 0.5em 0px 1.3em 1.4em; width: auto;"><div class="thumbinner" style="background-color: #f8f9fa; border: 1px solid rgb(200, 204, 209); display: flex; flex-direction: column; font-size: 13.16px; max-width: 492px; min-width: 100px; overflow: hidden; padding: 3px; text-align: center; width: 492px;"><div class="trow" style="box-sizing: border-box; clear: left; display: flex; flex-flow: wrap; width: 492px;"><div class="tsingle" style="float: left; margin: 1px; max-width: 187px; width: 187px;"><div class="thumbimage" style="border: 1px solid rgb(200, 204, 209); height: 185px; overflow: hidden;"><span typeof="mw:File"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:PDF-log_normal_distributions.svg" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;"><img alt="Tiga kurva fungsi kepadatan probabilitas yang asimetrik" class="mw-file-element" data-file-height="390" data-file-width="390" decoding="async" height="185" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/PDF-log_normal_distributions.svg/185px-PDF-log_normal_distributions.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/PDF-log_normal_distributions.svg/278px-PDF-log_normal_distributions.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/PDF-log_normal_distributions.svg/370px-PDF-log_normal_distributions.svg.png 2x" style="border: 0px; vertical-align: middle;" width="185" /></a></span></div><div class="thumbcaption" style="background-color: transparent; border: 0px; font-size: 12.3704px; line-height: 1.4em; padding: 3px; text-align: left;">Tiga <a href="https://id.wikipedia.org/wiki/Fungsi_kepekatan_probabilitas" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi kepekatan probabilitas">fungsi kepadatan probabilitas</a> (PDF) dari variabel acak dengan sebaran log-normal. Parameter lokasi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.5971px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">μ</span> yang bernilai nol untuk semua tiga fungsi tersebut, merupakan purata logaritma dari variabel acak, bukan purata dari variabel tersendiri.</div></div><div class="tsingle" style="float: left; margin: 1px; max-width: 301px; width: 301px;"><div class="thumbimage" style="border: 1px solid rgb(200, 204, 209); height: 185px; overflow: hidden;"><span typeof="mw:File"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Benfords_law_illustrated_by_world%27s_countries_population.png" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;"><img alt="A bar chart and a superimposed second chart. The two differ slightly, but both decrease in a similar fashion" class="mw-file-element" data-file-height="263" data-file-width="425" decoding="async" height="185" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Benfords_law_illustrated_by_world%27s_countries_population.png/299px-Benfords_law_illustrated_by_world%27s_countries_population.png" srcset="//upload.wikimedia.org/wikipedia/commons/0/0b/Benfords_law_illustrated_by_world%27s_countries_population.png 1.5x" style="border: 0px; vertical-align: middle;" width="299" /></a></span></div><div class="thumbcaption" style="background-color: transparent; border: 0px; font-size: 12.3704px; line-height: 1.4em; padding: 3px; text-align: left;">Sebaran digit pertama (dalam bentuk persentase, dengan batang berwarna merah) dalam <a href="https://id.wikipedia.org/wiki/Daftar_negara_menurut_jumlah_penduduk" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Daftar negara menurut jumlah penduduk">jumlah populasi dari 237 negara</a> di dunia. Titik berwarna hitam menunjukkan sebaran yang diprediksi menurut hukum Benford.</div></div></div></div></div><p style="margin: 0.5em 0px 1em;">Dalam <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Teori_probabilitas" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teori probabilitas">teori probabilitas</a>, <a class="new" href="https://id.wikipedia.org/w/index.php?title=Hukum_bilangan_besar&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Hukum bilangan besar (halaman belum tersedia)">hukum bilangan besar</a> mengatakan bahwa, untuk sebuah <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Mata_uang_seimbang" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Mata uang seimbang">mata uang seimbang</a>, ketika jumlah pelemparan koin naik menuju takhingga, maka kesebandingan dari gambar kepala (atau ekor) yang diamati <a href="https://id.wikipedia.org/wiki/Distribusi_binomial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Distribusi binomial">mendekati satu setengah</a>. Fluktuasi dari nilai kesebandingan yang bernilai satu setengah dijelaskan melalui hukum yang menggunakan logaritma, yaitu <a class="new" href="https://id.wikipedia.org/w/index.php?title=Hukum_logaritma_teriterasi&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Hukum logaritma teriterasi (halaman belum tersedia)">hukum logaritma teriterasi</a>.<sup class="reference" id="cite_ref-79" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-79" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[74]</a></sup></p><p style="margin: 0.5em 0px 1em;">Logaritma muncul pula dalam <a class="new" href="https://id.wikipedia.org/w/index.php?title=Sebaran_log-normal&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Sebaran log-normal (halaman belum tersedia)">sebaran log-normal</a>. Ketika logaritma dari <a href="https://id.wikipedia.org/wiki/Variabel_acak" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Variabel acak">variabel acak</a> mempunyai <a href="https://id.wikipedia.org/wiki/Distribusi_normal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Distribusi normal">sebaran normal</a>, maka variabel dikatakan mempunyai sebaran log-normal.<sup class="reference" id="cite_ref-80" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-80" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[75]</a></sup> Sebaran log-normal ditemukan dalam banyak bidang, dengan suatu variabel dibentuk sebagai hasil kali dari banyaknya variabel acak indenpenden bernilai positif. Contohnya seperti dalam mempelajari turbulensi.<sup class="reference" id="cite_ref-81" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-81" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[76]</a></sup></p><p style="margin: 0.5em 0px 1em;">Logaritma dipakai untuk menghitung <a class="new" href="https://id.wikipedia.org/w/index.php?title=Pendugaan_kemungkinan_maksimum&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Pendugaan kemungkinan maksimum (halaman belum tersedia)">estimasi kemungkinan maksimum</a> dari <a class="new" href="https://id.wikipedia.org/w/index.php?title=Model_statistika&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Model statistika (halaman belum tersedia)">model statistika</a> parametrik. <a class="new" href="https://id.wikipedia.org/w/index.php?title=Fungsi_kemungkinan&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi kemungkinan (halaman belum tersedia)">Fungsi kemungkinan</a> pada model tersebut bergantung setidaknya satu <a class="new" href="https://id.wikipedia.org/w/index.php?title=Model_parametrik&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Model parametrik (halaman belum tersedia)">parameter</a> yang harus diestimasi. Nilai maksimum dari fungsi kemungkinan muncul di nilai parameter yang sama sebagai nilai maksimum logaritma kemungkinan (atau disebut <i>log likelihood</i>), karena logaritma merupakan fungsi menaik. <i>Log-likelihood</i> adalah teknik yang memaksimumkan fungsi dengan mudah, khususnya untuk kemungkinan yang dikali mengenai variabel acak <a class="new" href="https://id.wikipedia.org/w/index.php?title=Independen_(peluang)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Independen (peluang) (halaman belum tersedia)">independen</a>.<sup class="reference" id="cite_ref-82" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-82" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[77]</a></sup></p><p style="margin: 0.5em 0px 1em;"><a href="https://id.wikipedia.org/wiki/Hukum_Benford" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Hukum Benford">Hukum Benford</a> menjelaskan kemungkinan digit dalam <a class="new" href="https://id.wikipedia.org/w/index.php?title=Himpunan_data&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Himpunan data (halaman belum tersedia)">himpunan data</a> yang banyak, contohnya seperti tinggi bangunan. Menurut hukum Benford, kemungkinan bahwa digit desimal pertama suatu item dalam sampel data adalah <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">d</span> (yang berkisar dari 1 hingga 9) sama dengan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;">10</sup>log (<i>d</i> + 1) − <sup style="font-size: 13.216px; line-height: 1;">10</sup>log (<i>d</i>)</span>, <i>tanpa memperhatikan</i> satuan pengukuran.<sup class="reference" id="cite_ref-83" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-83" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[78]</a></sup> Jadi, sekitar 30% data dapat diduga mempunyai 1 sebagai digit pertama, 18% dimulai dengan 2, dst. Penyimpangan dari hukum Benford dihitung oleh para akuntan untuk membantu mendeteksi penipuan data akuntansi.<sup class="reference" id="cite_ref-84" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-84" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[79]</a></sup></p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Penerapannya_dalam_kompleksitas_perhitungan">Penerapannya dalam kompleksitas perhitungan</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=29" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Penerapannya dalam kompleksitas perhitungan">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=29" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Penerapannya dalam kompleksitas perhitungan">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;">Cabang dalam <a href="https://id.wikipedia.org/wiki/Ilmu_komputer" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Ilmu komputer">ilmu komputer</a> yang mempelajari <a href="https://id.wikipedia.org/wiki/Kompleksitas_waktu" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kompleksitas waktu">performa</a> dari suatu <a href="https://id.wikipedia.org/wiki/Algoritma" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Algoritma">algoritma</a> dalam menyelesaikan persoalan atau masalah tertentu disebut <a class="new" href="https://id.wikipedia.org/w/index.php?title=Analisis_algoritma&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Analisis algoritma (halaman belum tersedia)">analisis algoritma</a>.<sup class="reference" id="cite_ref-Wegener_85-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-Wegener-85" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[80]</a></sup> Logaritma sangat penting dalam menjelaskan algoritma tersebut dengan <a href="https://id.wikipedia.org/wiki/Divide_and_Conquer" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Divide and Conquer">membagi suatu masalah</a> menjadi lebih kecil, serta menghubungkan penyelesaian dari submasalah.<sup class="reference" id="cite_ref-86" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-86" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[81]</a></sup></p><p style="margin: 0.5em 0px 1em;">Sebagai contoh, cara <a href="https://id.wikipedia.org/wiki/Algoritma_pencarian_biner" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Algoritma pencarian biner">algoritma pencarian biner</a> (<a href="https://id.wikipedia.org/wiki/Bahasa_Inggris" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bahasa Inggris">bahasa Inggris</a>: <span lang="en"><i>binary searching algorithm</i></span>) dalam mencari bilangan dalam daftar yang tersortir adalah dengan memeriksa entri tengah dan meneruskannya di sebagian sebelum atau sesudah entri tengah jika tidak ditemukan bilangannya. Umumnya, algoritma ini memerlukan perbandingan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;">2</sup>log (<i>N</i>)</span>, dengan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">N</span> adalah panjang daftar.<sup class="reference" id="cite_ref-87" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-87" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[82]</a></sup> Mirip dengan sebelumnya, algoritma <a href="https://id.wikipedia.org/wiki/Urut_gabung" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Urut gabung">urut gabungan</a> menyortir daftar yang belum tersortir dengan membagi daftar menjadi setengah bagian dan mengurutkan daftar-daftar tersebut dahulu sebelum menggabungkan hasilnya. Algoritma urut gabungan biasanya memerlukan waktu yang <a href="https://id.wikipedia.org/wiki/Notasi_O_besar" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Notasi O besar">kira-kira sebanding dengan</a> <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>N</i> · log(<i>N</i>)</span>.<sup class="reference" id="cite_ref-88" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-88" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[83]</a></sup> Bilangan pokok logaritma tidak dijelaskan secara spesifik, karena hasilnya hanya berubah oleh faktor konstanta saat ada bilangan pokok lain yang sedang dipakai. Faktor konstanta biasanya diabaikan dalam analisis algoritma dalam <a class="new" href="https://id.wikipedia.org/w/index.php?title=Analisis_algoritma&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Analisis algoritma (halaman belum tersedia)">model biaya seragam</a> (<a href="https://id.wikipedia.org/wiki/Bahasa_Inggris" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bahasa Inggris">bahasa Inggris</a>: <span lang="en"><i>uniform cost model</i></span>) yang standar.<sup class="reference" id="cite_ref-Wegener20_89-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-Wegener20-89" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[84]</a></sup></p><p style="margin: 0.5em 0px 1em;">Suatu fungsi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f</i>(<i>x</i>)</span> dikatakan <a href="https://id.wikipedia.org/wiki/Pertumbuhan_logaritmik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Pertumbuhan logaritmik">bertumbuh secara logaritmik</a> jika <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f</i>(<i>x</i>)</span> (setidaknya atau kira-kira) sebanding dengan logaritma dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>, namun istilah ini dipakai sebagai fungsi eksponensial dalam menjelaskan pertumbuhan organisme secara biologis.<sup class="reference" id="cite_ref-90" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-90" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[85]</a></sup> Sebagai contoh, setiap <a href="https://id.wikipedia.org/wiki/Bilangan_asli" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan asli">bilangan asli</a> <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">N</span> dapat direpresentasikan dalam <a href="https://id.wikipedia.org/wiki/Sistem_bilangan_biner" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Sistem bilangan biner">bentuk bilangan biner</a> yang tidak lebih dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;">2</sup>log <i>N</i> + 1</span> <a class="mw-disambig" href="https://id.wikipedia.org/wiki/Bit" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bit">bit</a>. Dengan kata lain, jumlah <a href="https://id.wikipedia.org/wiki/Memori_(komputer)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Memori (komputer)">memori</a> diperlukan untuk menyimpan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">N</span> pertumbuhan secara logaritmik dengan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">N</span>.</p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Penerapannya_dalam_entropi_dan_ketidakteraturan">Penerapannya dalam entropi dan ketidakteraturan</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=30" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Penerapannya dalam entropi dan ketidakteraturan">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=30" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Penerapannya dalam entropi dan ketidakteraturan">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><figure class="mw-default-size" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Chaotic_Bunimovich_stadium.png" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img alt="Trayektori dua partikel berbentuk oval" class="mw-file-element" data-file-height="379" data-file-width="758" decoding="async" height="110" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Chaotic_Bunimovich_stadium.png/220px-Chaotic_Bunimovich_stadium.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Chaotic_Bunimovich_stadium.png/330px-Chaotic_Bunimovich_stadium.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Chaotic_Bunimovich_stadium.png/440px-Chaotic_Bunimovich_stadium.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="220" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;"><a href="https://id.wikipedia.org/wiki/Biliar_dinamis" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Biliar dinamis">Bola biliar</a> di atas meja biliar oval. Dua partikel yang bermula pada pusat meja dengan sudut luncur yang berbeda satu derajat, akan memiliki jalur yang amat berbeda karena <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Refleksi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Refleksi">pemantulan</a> pada pinggir meja biliar</figcaption></figure><p style="margin: 0.5em 0px 1em;"><a href="https://id.wikipedia.org/wiki/Entropi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Entropi">Entropi</a> secara umum adalah ukuran dari ketidakteraturan dari suatu sistem. Dalam <a href="https://id.wikipedia.org/wiki/Termodinamika_statistik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Termodinamika statistik">termodinamika statistik</a>, sebuah entropi, disimbolkan dengan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>S</i></span>, dari sebuah sistem, didefinisikan dengan:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle S=-k\sum _{i}p_{i}\ln(p_{i}).\,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><mo>−</mo><mi>�</mi><munder><mo>∑</mo><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></munder><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo stretchy="false">)</mo><mo>.</mo><mspace width="thinmathspace"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle S=-k\sum _{i}p_{i}\ln(p_{i}).\,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4be67693caef12b846ed9cd173a0e7a340364d27" style="border: 0px; display: inline-block; height: 5.509ex; vertical-align: -3.005ex; width: 20.854ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Hasilnya adalah seluruh kondisi <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">i</span> yang mungkin dari sistem yang dimaksud, contoh posisi dari partikel gas di dalam sebuah tangki. Lebih lanjut lagi, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>p</i><sub style="font-size: 13.216px; line-height: 1;"><i>i</i></sub></span> adalah kemungkinan bahwa kondisi <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">i</span> telah tercapai dan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">k</span> adalah <a href="https://id.wikipedia.org/wiki/Konstanta_Boltzmann" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Konstanta Boltzmann">konstanta Boltzmann</a>. Sama halnya dengan <a href="https://id.wikipedia.org/wiki/Entropi_(teori_informasi)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Entropi (teori informasi)">entropi dalam teori informasi</a> yang mengukur kuantitas dari informasi. Jika penerima pesan mengharapkan sejumlah <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">N</span> pesan yang mungkin diterima dengan besar kemungkinan masing-masing yang setara, maka sejumlah informasi yang tersampaikan oleh pesan tersebut dapat dikuantifikasi dengan bit <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><sup style="font-size: 13.216px; line-height: 1;">2</sup>log <i>N</i></span>.<sup class="reference" id="cite_ref-91" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-91" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[86]</a></sup></p><p style="margin: 0.5em 0px 1em;"><a class="new" href="https://id.wikipedia.org/w/index.php?title=Eksponen_Lyapunov&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Eksponen Lyapunov (halaman belum tersedia)">Eksponen Lyapunov</a> menggunakan logaritma untuk mengukur derajat ketidakteraturan dari sistem yang dinamis. Contoh partikel yang bergerak di meja biliar oval, di mana bahkan perubahan sekecil apapun dari kondisi awal dapat memberikan hasil, yaitu jalur yang dilalui, yang sangat berbeda. Sistem yang dimaksud disebut dengan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Teori_chaos" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teori chaos">kekacauan</a> di dalam <a href="https://id.wikipedia.org/wiki/Sistem_deterministik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Sistem deterministik">sistem deterministik</a> karena galat yang kecil namun terukur dari kondisi awal dapat diprediksi akan memberikan hasil akhir yang sangat berbeda.<sup class="reference" id="cite_ref-92" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-92" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[87]</a></sup> Setidaknya satu eksponen Lyapunov dari sistem kekacauan yang deterministik akan bernilai positif.</p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Penerapannya_dalam_bangunan_fraktal">Penerapannya dalam bangunan fraktal</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=31" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Penerapannya dalam bangunan fraktal">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=31" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Penerapannya dalam bangunan fraktal">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><figure class="mw-halign-right" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Sierpinski_dimension.svg" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img alt="Parts of a triangle are removed in an iterated way." class="mw-file-element" data-file-height="108" data-file-width="745" decoding="async" height="58" src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/37/Sierpinski_dimension.svg/400px-Sierpinski_dimension.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Sierpinski_dimension.svg/600px-Sierpinski_dimension.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/Sierpinski_dimension.svg/800px-Sierpinski_dimension.svg.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="400" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Segitiga Sierpinski (di sebelah kanan) dibangun dengan menggantikan <a href="https://id.wikipedia.org/wiki/Segitiga_sama_sisi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Segitiga sama sisi">segitiga sama sisi</a> secara berulang dengan tiga salinan dirinya yang lebih kecil.</figcaption></figure><p style="margin: 0.5em 0px 1em;">Logaritma muncul dalam definiisi <a href="https://id.wikipedia.org/wiki/Dimensi_fraktal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Dimensi fraktal">dimensi</a> <a href="https://id.wikipedia.org/wiki/Fraktal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fraktal">fraktal</a>.<sup class="reference" id="cite_ref-93" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-93" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[88]</a></sup> Fraktal merupakan benda-benda geometri yang menyerupai dirinya, dalam artian bahwa benda geometri tersebut mereproduksi dirinya lebih kecil, penjelasan kasarnya, di seluruh strukturnya. Contohnya seperti <a href="https://id.wikipedia.org/wiki/Segitiga_Sierpi%C5%84ski" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Segitiga Sierpiński">segitiga Sierpiński</a>, dengan <a href="https://id.wikipedia.org/wiki/Dimensi_Hausdorff" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Dimensi Hausdorff">dimensi Hausdorff</a>nya adalah <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><span class="sfrac nowrap" style="display: inline-block; font-size: 14.042px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;">ln(3)</span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;">ln(2)</span></span> ≈ 1,58</span>, dapat diliputi dengan tiga salinan dirinya, masing-masing sisinya dibagi menjadi setengah dari panjang awalnya. Adapula gagasan dimensi fraktal berdasarkan logaritma lainnya diperoleh dengan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Dimensi_menghitung_kotak" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Dimensi menghitung kotak">menghitung jumlah kotak</a> yang diperlukan untuk meliputi frakal dalam himpunan.</p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Penerapannya_dalam_musik">Penerapannya dalam musik</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=32" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Penerapannya dalam musik">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=32" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Penerapannya dalam musik">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><div class="thumb tmulti tright" style="background-color: transparent; clear: right; float: right; margin: 0.5em 0px 1.3em 1.4em; width: auto;"><div class="thumbinner" style="background-color: #f8f9fa; border: 1px solid rgb(200, 204, 209); display: flex; flex-direction: column; font-size: 13.16px; max-width: 354px; min-width: 100px; overflow: hidden; padding: 3px; text-align: center; width: 354px;"><div class="trow" style="box-sizing: border-box; clear: left; display: flex; flex-flow: wrap; width: 354px;"><div class="tsingle" style="float: left; margin: 1px; max-width: 352px; width: 352px;"><div class="thumbimage" style="border: 1px solid rgb(200, 204, 209);"><span typeof="mw:File"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:4Octaves.and.Frequencies.svg" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;"><img alt="Empat oktaf yang berbeda diperlihatkan pada skala linear." class="mw-file-element" data-file-height="72" data-file-width="670" decoding="async" height="38" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/13/4Octaves.and.Frequencies.svg/350px-4Octaves.and.Frequencies.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/4Octaves.and.Frequencies.svg/525px-4Octaves.and.Frequencies.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/13/4Octaves.and.Frequencies.svg/700px-4Octaves.and.Frequencies.svg.png 2x" style="border: 0px; vertical-align: middle;" width="350" /></a></span></div></div></div><div class="trow" style="box-sizing: border-box; clear: left; display: flex; flex-flow: wrap; width: 354px;"><div class="tsingle" style="float: left; margin: 1px; max-width: 352px; width: 352px;"><div class="thumbimage" style="border: 1px solid rgb(200, 204, 209);"><span typeof="mw:File"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:4Octaves.and.Frequencies.Ears.svg" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;"><img alt="Empat oktaf yang berbeda diperlihatkan pada skala logaritmik." class="mw-file-element" data-file-height="74" data-file-width="578" decoding="async" height="45" src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/31/4Octaves.and.Frequencies.Ears.svg/350px-4Octaves.and.Frequencies.Ears.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/4Octaves.and.Frequencies.Ears.svg/525px-4Octaves.and.Frequencies.Ears.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/31/4Octaves.and.Frequencies.Ears.svg/700px-4Octaves.and.Frequencies.Ears.svg.png 2x" style="border: 0px; vertical-align: middle;" width="350" /></a></span></div></div></div><div class="trow" style="box-sizing: border-box; clear: left; display: flex; flex-flow: wrap; width: 354px;"><div class="thumbcaption" style="background-color: transparent; border: 0px; font-size: 12.3704px; line-height: 1.4em; padding: 3px; text-align: left;">Empat oktaf yang berbeda diperlihatkan pada skala linear, lalu diperlihatkan pada skala logaritmik (saat mendengarkannya dengan menggunakan telinga).</div></div></div></div><p style="margin: 0.5em 0px 1em;">Logaritma berkaitan dengan bunyi nada dan <a href="https://id.wikipedia.org/wiki/Interval_(musik)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Interval (musik)">interval</a> dalam musik. Dalam <a class="new" href="https://id.wikipedia.org/w/index.php?title=Temperamen_sama&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Temperamen sama (halaman belum tersedia)">temperamen sama</a>, perbandingan frekuensi bergantung pada interval di antara dua nada saja, bukan pada frekuensi yang spesifik atau <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Tinggi_nada" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Tinggi nada">tinggi</a> dari nada tunggal. Sebagai contoh, nada <a class="new" href="https://id.wikipedia.org/w/index.php?title=A_(not_musik)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="A (not musik) (halaman belum tersedia)"><i>A</i></a> mempunyai frekuensi 440 <a href="https://id.wikipedia.org/wiki/Hertz" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Hertz">Hz</a> dan <a class="new" href="https://id.wikipedia.org/w/index.php?title=B%E2%99%AD_(not_musik)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="B♭ (not musik) (halaman belum tersedia)"><i>B-flat</i></a> mempunyai frekuensi 466 Hz. Interval antara nada <i>A</i> dengan <i>B-flat</i> ini digolongkan sebagai <a class="new" href="https://id.wikipedia.org/w/index.php?title=Semi-nada&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Semi-nada (halaman belum tersedia)">semi-nada</a>, karena intervalnya berada di antara <i>B-flat</i> dan <a class="new" href="https://id.wikipedia.org/w/index.php?title=B_(not_musik)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="B (not musik) (halaman belum tersedia)"><i>B</i></a> (yang mempunyai frekuensi 493 Hz). Maka, perbandingan frekuensinya adalah:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\frac {466}{440}}\approx {\frac {493}{466}}\approx 1,059\approx {\sqrt[{12}]{2}}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>466</mn><mn>440</mn></mfrac></mrow><mo>≈</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>493</mn><mn>466</mn></mfrac></mrow><mo>≈</mo><mn>1</mn><mo>,</mo><mn>059</mn><mo>≈</mo><mrow class="MJX-TeXAtom-ORD"><mroot><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mn>12</mn></mrow></mroot></mrow><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\frac {466}{440}}\approx {\frac {493}{466}}\approx 1,059\approx {\sqrt[{12}]{2}}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a4a4571d8dc6ff40e6042496a3a6393c6d4a8b99" style="border: 0px; display: inline-block; height: 5.343ex; vertical-align: -2.005ex; width: 27.38ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Peran logaritma dalam musik dapat dipakai untuk menjelaskan interval berikut: suatu interval diukur dalam semi-nada dengan mengambil logaritma dengan <span class="nowrap" style="text-wrap: nowrap;">bilangan pokok-<span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">2<sup style="font-size: 13.216px; line-height: 1;">1/12</sup></span></span> dari perbandingan <a href="https://id.wikipedia.org/wiki/Frekuensi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Frekuensi">frekuensi</a>, sedangkan logaritma dengan <span class="nowrap" style="text-wrap: nowrap;">bilangan pokok-<span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">2<sup style="font-size: 13.216px; line-height: 1;">1/1200</sup></span></span> dari perbandingan frekuensi menyatakan interval dalam <a href="https://id.wikipedia.org/wiki/Sen_(musik)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Sen (musik)">sen</a>, ratusan semi-nada. Logaritma yang terakhir dipakai untuk pengodean yang lebih halus, karena diperlukan untuk temperamen tak sama.<sup class="reference" id="cite_ref-94" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-94" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[89]</a></sup></p><table class="wikitable" style="background-color: #f8f9fa; border-collapse: collapse; border: 1px solid rgb(162, 169, 177); color: #202122; font-size: 14px; margin: 1em auto; text-align: center;"><tbody><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><b>Interval</b> (dua bunyi nada yang dimainkan dalam waktu yang sama)</td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><a class="new" href="https://id.wikipedia.org/w/index.php?title=72_temperamen_sama&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="72 temperamen sama (halaman belum tersedia)">Bunyi nada 1/12</a> <span class="ext-phonos" style="text-wrap: nowrap;"><span class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-nosnippet="" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/b\/b8\/1_step_in_72-et_on_C.mid\/1_step_in_72-et_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"id","wikibase":"","file":"1 step in 72-et on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}" id="ooui-php-1" style="margin: 0px; vertical-align: baseline;"><a aria-label="Putar audio" class="oo-ui-buttonElement-button" href="https://upload.wikimedia.org/wikipedia/commons/transcoded/b/b8/1_step_in_72-et_on_C.mid/1_step_in_72-et_on_C.mid.mp3" rel="nofollow" role="button" style="background: none; color: #3366cc; display: inline; min-height: 22px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-decoration-line: none; user-select: auto; vertical-align: baseline;" tabindex="0" title="Putar audio"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp" style="background-image: url("data:image/svg+xml,%3Csvg xmlns=%22http://www.w3.org/2000/svg%22 width=%2220%22 height=%2220%22 viewBox=%220 0 20 20%22%3E%3Ctitle%3E volume up %3C/title%3E%3Cpath d=%22M4 6v8l5.2 3.9c.3.3.8 0 .8-.5V2.6c0-.5-.5-.8-.8-.5zm0 8H1a1 1 0 0 1-1-1V7a1 1 0 0 1 1-1h3m12.4 11.4a1 1 0 0 1-.7-1.7 8 8 0 0 0 0-11.4A1 1 0 0 1 17 3a10 10 0 0 1 0 14.2 1 1 0 0 1-.7.3z%22/%3E%3Cpath d=%22M13.5 14.5a1 1 0 0 1-.7-.3 1 1 0 0 1 0-1.4 4 4 0 0 0 0-5.6 1 1 0 0 1 1.4-1.4 6 6 0 0 1 0 8.4 1 1 0 0 1-.7.3%22/%3E%3C/svg%3E"); background-position: left center; background-size: cover; display: inline-block; height: 1em; left: 0px; min-height: 0px; min-width: 0px; position: relative; top: 0.1em; width: 1em;"></span><span class="oo-ui-labelElement-label" style="display: inline-block; margin-inline-start: 0.3em;">play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable" style="font-size: 11.2px; line-height: 1; margin-inline-start: 3px;"><a href="https://id.wikipedia.org/wiki/Berkas:1_step_in_72-et_on_C.mid" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Berkas:1 step in 72-et on C.mid">ⓘ</a></sup></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><a class="new" href="https://id.wikipedia.org/w/index.php?title=Semi-nada&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Semi-nada (halaman belum tersedia)">Semi-nada</a> <span class="ext-phonos" style="text-wrap: nowrap;"><span class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-nosnippet="" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/8\/8a\/Minor_second_on_C.mid\/Minor_second_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"id","wikibase":"","file":"Minor second on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}" id="ooui-php-2" style="margin: 0px; vertical-align: baseline;"><a aria-label="Putar audio" class="oo-ui-buttonElement-button" href="https://upload.wikimedia.org/wikipedia/commons/transcoded/8/8a/Minor_second_on_C.mid/Minor_second_on_C.mid.mp3" rel="nofollow" role="button" style="background: none; color: #3366cc; display: inline; min-height: 22px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-decoration-line: none; user-select: auto; vertical-align: baseline;" tabindex="0" title="Putar audio"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp" style="background-image: url("data:image/svg+xml,%3Csvg xmlns=%22http://www.w3.org/2000/svg%22 width=%2220%22 height=%2220%22 viewBox=%220 0 20 20%22%3E%3Ctitle%3E volume up %3C/title%3E%3Cpath d=%22M4 6v8l5.2 3.9c.3.3.8 0 .8-.5V2.6c0-.5-.5-.8-.8-.5zm0 8H1a1 1 0 0 1-1-1V7a1 1 0 0 1 1-1h3m12.4 11.4a1 1 0 0 1-.7-1.7 8 8 0 0 0 0-11.4A1 1 0 0 1 17 3a10 10 0 0 1 0 14.2 1 1 0 0 1-.7.3z%22/%3E%3Cpath d=%22M13.5 14.5a1 1 0 0 1-.7-.3 1 1 0 0 1 0-1.4 4 4 0 0 0 0-5.6 1 1 0 0 1 1.4-1.4 6 6 0 0 1 0 8.4 1 1 0 0 1-.7.3%22/%3E%3C/svg%3E"); background-position: left center; background-size: cover; display: inline-block; height: 1em; left: 0px; min-height: 0px; min-width: 0px; position: relative; top: 0.1em; width: 1em;"></span><span class="oo-ui-labelElement-label" style="display: inline-block; margin-inline-start: 0.3em;">play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable" style="font-size: 11.2px; line-height: 1; margin-inline-start: 3px;"><a href="https://id.wikipedia.org/wiki/Berkas:Minor_second_on_C.mid" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Berkas:Minor second on C.mid">ⓘ</a></sup></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><i><a class="new" href="https://id.wikipedia.org/w/index.php?title=Just_major_third&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Just major third (halaman belum tersedia)">Just major third</a></i> <span class="ext-phonos" style="text-wrap: nowrap;"><span class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-nosnippet="" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/2\/2a\/Just_major_third_on_C.mid\/Just_major_third_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"id","wikibase":"","file":"Just major third on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}" id="ooui-php-3" style="margin: 0px; vertical-align: baseline;"><a aria-label="Putar audio" class="oo-ui-buttonElement-button" href="https://upload.wikimedia.org/wikipedia/commons/transcoded/2/2a/Just_major_third_on_C.mid/Just_major_third_on_C.mid.mp3" rel="nofollow" role="button" style="background: none; color: #3366cc; display: inline; min-height: 22px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-decoration-line: none; user-select: auto; vertical-align: baseline;" tabindex="0" title="Putar audio"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp" style="background-image: url("data:image/svg+xml,%3Csvg xmlns=%22http://www.w3.org/2000/svg%22 width=%2220%22 height=%2220%22 viewBox=%220 0 20 20%22%3E%3Ctitle%3E volume up %3C/title%3E%3Cpath d=%22M4 6v8l5.2 3.9c.3.3.8 0 .8-.5V2.6c0-.5-.5-.8-.8-.5zm0 8H1a1 1 0 0 1-1-1V7a1 1 0 0 1 1-1h3m12.4 11.4a1 1 0 0 1-.7-1.7 8 8 0 0 0 0-11.4A1 1 0 0 1 17 3a10 10 0 0 1 0 14.2 1 1 0 0 1-.7.3z%22/%3E%3Cpath d=%22M13.5 14.5a1 1 0 0 1-.7-.3 1 1 0 0 1 0-1.4 4 4 0 0 0 0-5.6 1 1 0 0 1 1.4-1.4 6 6 0 0 1 0 8.4 1 1 0 0 1-.7.3%22/%3E%3C/svg%3E"); background-position: left center; background-size: cover; display: inline-block; height: 1em; left: 0px; min-height: 0px; min-width: 0px; position: relative; top: 0.1em; width: 1em;"></span><span class="oo-ui-labelElement-label" style="display: inline-block; margin-inline-start: 0.3em;">play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable" style="font-size: 11.2px; line-height: 1; margin-inline-start: 3px;"><a href="https://id.wikipedia.org/wiki/Berkas:Just_major_third_on_C.mid" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Berkas:Just major third on C.mid">ⓘ</a></sup></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><i><a class="new" href="https://id.wikipedia.org/w/index.php?title=Major_third&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Major third (halaman belum tersedia)">Major third</a></i> <span class="ext-phonos" style="text-wrap: nowrap;"><span class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-nosnippet="" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/9\/91\/Major_third_on_C.mid\/Major_third_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"id","wikibase":"","file":"Major third on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}" id="ooui-php-4" style="margin: 0px; vertical-align: baseline;"><a aria-label="Putar audio" class="oo-ui-buttonElement-button" href="https://upload.wikimedia.org/wikipedia/commons/transcoded/9/91/Major_third_on_C.mid/Major_third_on_C.mid.mp3" rel="nofollow" role="button" style="background: none; color: #3366cc; display: inline; min-height: 22px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-decoration-line: none; user-select: auto; vertical-align: baseline;" tabindex="0" title="Putar audio"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp" style="background-image: url("data:image/svg+xml,%3Csvg xmlns=%22http://www.w3.org/2000/svg%22 width=%2220%22 height=%2220%22 viewBox=%220 0 20 20%22%3E%3Ctitle%3E volume up %3C/title%3E%3Cpath d=%22M4 6v8l5.2 3.9c.3.3.8 0 .8-.5V2.6c0-.5-.5-.8-.8-.5zm0 8H1a1 1 0 0 1-1-1V7a1 1 0 0 1 1-1h3m12.4 11.4a1 1 0 0 1-.7-1.7 8 8 0 0 0 0-11.4A1 1 0 0 1 17 3a10 10 0 0 1 0 14.2 1 1 0 0 1-.7.3z%22/%3E%3Cpath d=%22M13.5 14.5a1 1 0 0 1-.7-.3 1 1 0 0 1 0-1.4 4 4 0 0 0 0-5.6 1 1 0 0 1 1.4-1.4 6 6 0 0 1 0 8.4 1 1 0 0 1-.7.3%22/%3E%3C/svg%3E"); background-position: left center; background-size: cover; display: inline-block; height: 1em; left: 0px; min-height: 0px; min-width: 0px; position: relative; top: 0.1em; width: 1em;"></span><span class="oo-ui-labelElement-label" style="display: inline-block; margin-inline-start: 0.3em;">play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable" style="font-size: 11.2px; line-height: 1; margin-inline-start: 3px;"><a href="https://id.wikipedia.org/wiki/Berkas:Major_third_on_C.mid" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Berkas:Major third on C.mid">ⓘ</a></sup></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><i><a class="new" href="https://id.wikipedia.org/w/index.php?title=Tritone&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Tritone (halaman belum tersedia)">Tritone</a></i> <span class="ext-phonos" style="text-wrap: nowrap;"><span class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-nosnippet="" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/5\/58\/Tritone_on_C.mid\/Tritone_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"id","wikibase":"","file":"Tritone on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}" id="ooui-php-5" style="margin: 0px; vertical-align: baseline;"><a aria-label="Putar audio" class="oo-ui-buttonElement-button" href="https://upload.wikimedia.org/wikipedia/commons/transcoded/5/58/Tritone_on_C.mid/Tritone_on_C.mid.mp3" rel="nofollow" role="button" style="background: none; color: #3366cc; display: inline; min-height: 22px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-decoration-line: none; user-select: auto; vertical-align: baseline;" tabindex="0" title="Putar audio"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp" style="background-image: url("data:image/svg+xml,%3Csvg xmlns=%22http://www.w3.org/2000/svg%22 width=%2220%22 height=%2220%22 viewBox=%220 0 20 20%22%3E%3Ctitle%3E volume up %3C/title%3E%3Cpath d=%22M4 6v8l5.2 3.9c.3.3.8 0 .8-.5V2.6c0-.5-.5-.8-.8-.5zm0 8H1a1 1 0 0 1-1-1V7a1 1 0 0 1 1-1h3m12.4 11.4a1 1 0 0 1-.7-1.7 8 8 0 0 0 0-11.4A1 1 0 0 1 17 3a10 10 0 0 1 0 14.2 1 1 0 0 1-.7.3z%22/%3E%3Cpath d=%22M13.5 14.5a1 1 0 0 1-.7-.3 1 1 0 0 1 0-1.4 4 4 0 0 0 0-5.6 1 1 0 0 1 1.4-1.4 6 6 0 0 1 0 8.4 1 1 0 0 1-.7.3%22/%3E%3C/svg%3E"); background-position: left center; background-size: cover; display: inline-block; height: 1em; left: 0px; min-height: 0px; min-width: 0px; position: relative; top: 0.1em; width: 1em;"></span><span class="oo-ui-labelElement-label" style="display: inline-block; margin-inline-start: 0.3em;">play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable" style="font-size: 11.2px; line-height: 1; margin-inline-start: 3px;"><a href="https://id.wikipedia.org/wiki/Berkas:Tritone_on_C.mid" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Berkas:Tritone on C.mid">ⓘ</a></sup></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><a href="https://id.wikipedia.org/wiki/Oktaf" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Oktaf">Oktaf</a> <span class="ext-phonos" style="text-wrap: nowrap;"><span class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-nosnippet="" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/f\/f0\/Perfect_octave_on_C.mid\/Perfect_octave_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"id","wikibase":"","file":"Perfect octave on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}" id="ooui-php-6" style="margin: 0px; vertical-align: baseline;"><a aria-label="Putar audio" class="oo-ui-buttonElement-button" href="https://upload.wikimedia.org/wikipedia/commons/transcoded/f/f0/Perfect_octave_on_C.mid/Perfect_octave_on_C.mid.mp3" rel="nofollow" role="button" style="background: none; color: #3366cc; display: inline; min-height: 22px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-decoration-line: none; user-select: auto; vertical-align: baseline;" tabindex="0" title="Putar audio"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp" style="background-image: url("data:image/svg+xml,%3Csvg xmlns=%22http://www.w3.org/2000/svg%22 width=%2220%22 height=%2220%22 viewBox=%220 0 20 20%22%3E%3Ctitle%3E volume up %3C/title%3E%3Cpath d=%22M4 6v8l5.2 3.9c.3.3.8 0 .8-.5V2.6c0-.5-.5-.8-.8-.5zm0 8H1a1 1 0 0 1-1-1V7a1 1 0 0 1 1-1h3m12.4 11.4a1 1 0 0 1-.7-1.7 8 8 0 0 0 0-11.4A1 1 0 0 1 17 3a10 10 0 0 1 0 14.2 1 1 0 0 1-.7.3z%22/%3E%3Cpath d=%22M13.5 14.5a1 1 0 0 1-.7-.3 1 1 0 0 1 0-1.4 4 4 0 0 0 0-5.6 1 1 0 0 1 1.4-1.4 6 6 0 0 1 0 8.4 1 1 0 0 1-.7.3%22/%3E%3C/svg%3E"); background-position: left center; background-size: cover; display: inline-block; height: 1em; left: 0px; min-height: 0px; min-width: 0px; position: relative; top: 0.1em; width: 1em;"></span><span class="oo-ui-labelElement-label" style="display: inline-block; margin-inline-start: 0.3em;">play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable" style="font-size: 11.2px; line-height: 1; margin-inline-start: 3px;"><a href="https://id.wikipedia.org/wiki/Berkas:Perfect_octave_on_C.mid" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Berkas:Perfect octave on C.mid">ⓘ</a></sup></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><b>Rasio frekuensi</b> <i>r</i></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 2^{\frac {1}{72}}\approx 1.0097}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mn>72</mn></mfrac></mrow></msup><mo>≈</mo><mn>1.0097</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 2^{\frac {1}{72}}\approx 1.0097}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dcce5a9aa9e216fc208a597f74d2d2b6248663e6" style="border: 0px; display: inline-block; height: 3.509ex; vertical-align: -0.338ex; width: 13.123ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 2^{\frac {1}{12}}\approx 1.0595}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mn>12</mn></mfrac></mrow></msup><mo>≈</mo><mn>1.0595</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 2^{\frac {1}{12}}\approx 1.0595}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18664eeb9dbe129067dd89295c4928d54fda5f01" style="border: 0px; display: inline-block; height: 3.509ex; vertical-align: -0.338ex; width: 13.123ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\tfrac {5}{4}}=1.25}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mn>5</mn><mn>4</mn></mfrac></mstyle></mrow><mo>=</mo><mn>1.25</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\tfrac {5}{4}}=1.25}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84da6d3ba8b361f151624067f68d609526e6e47b" style="border: 0px; display: inline-block; height: 3.509ex; vertical-align: -1.171ex; width: 8.891ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\begin{aligned}2^{\frac {4}{12}}&={\sqrt[{3}]{2}}\\&\approx 1.2599\end{aligned}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd><msup><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>4</mn><mn>12</mn></mfrac></mrow></msup></mtd><mtd><mi></mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mroot><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></mroot></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>≈</mo><mn>1.2599</mn></mtd></mtr></mtable></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\begin{aligned}2^{\frac {4}{12}}&={\sqrt[{3}]{2}}\\&\approx 1.2599\end{aligned}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76610ca7878ea438fa73bd50ac4df1fecce09b9f" style="border: 0px; display: inline-block; height: 6.843ex; vertical-align: -2.838ex; width: 13.875ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\begin{aligned}2^{\frac {6}{12}}&={\sqrt {2}}\\&\approx 1.4142\end{aligned}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd><msup><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>6</mn><mn>12</mn></mfrac></mrow></msup></mtd><mtd><mi></mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><msqrt><mn>2</mn></msqrt></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>≈</mo><mn>1.4142</mn></mtd></mtr></mtable></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\begin{aligned}2^{\frac {6}{12}}&={\sqrt {2}}\\&\approx 1.4142\end{aligned}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa178821ca7a1554106bf2244d08577f6f5d17fb" style="border: 0px; display: inline-block; height: 6.843ex; vertical-align: -2.838ex; width: 13.875ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 2^{\frac {12}{12}}=2}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>12</mn><mn>12</mn></mfrac></mrow></msup><mo>=</mo><mn>2</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 2^{\frac {12}{12}}=2}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0b7cc906bb2bc2787e32f7d1643b290d7b96766" style="border: 0px; display: inline-block; height: 3.509ex; vertical-align: -0.338ex; width: 7.826ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><b>Jumlah semi-nada yang sama</b><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ^{\sqrt[{12}]{2}}\!\log r=12\,^{2}\!\log r}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mroot><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mn>12</mn></mrow></mroot></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mo>=</mo><mn>12</mn><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ^{\sqrt[{12}]{2}}\!\log r=12\,^{2}\!\log r}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbbff697ad50b2a11b9dd950a993569e9fbd687e" style="border: 0px; display: inline-block; height: 3.676ex; vertical-align: -0.671ex; width: 18.48ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\tfrac {1}{6}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mn>1</mn><mn>6</mn></mfrac></mstyle></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\tfrac {1}{6}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bc02e655226b1a0e18922e932efff50531c48eb" style="border: 0px; display: inline-block; height: 3.676ex; vertical-align: -1.338ex; width: 1.658ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 1}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>1</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 1}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" style="border: 0px; display: inline-block; height: 2.176ex; vertical-align: -0.338ex; width: 1.162ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \approx 3,8631}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>≈</mo><mn>3</mn><mo>,</mo><mn>8631</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \approx 3,8631}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47d544e184b32e3e948141684717e883e88b3d1e" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 9.3ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 4}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>4</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 4}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/295b4bf1de7cd3500e740e0f4f0635db22d87b42" style="border: 0px; display: inline-block; height: 2.176ex; vertical-align: -0.338ex; width: 1.162ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 6}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>6</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 6}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39d81124420a058a7474dfeda48228fb6ee1e253" style="border: 0px; display: inline-block; height: 2.176ex; vertical-align: -0.338ex; width: 1.162ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 12}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>12</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 12}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a522d3aa5812a136a69f06e1b909d809e849be39" style="border: 0px; display: inline-block; height: 2.176ex; vertical-align: -0.338ex; width: 2.325ex;" /></span></td></tr><tr><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><b>Jumlah sen yang sama</b><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle ^{\sqrt[{1200}]{2}}\!\log r=1200\,^{2}\!\log r}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mroot><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mn>1200</mn></mrow></mroot></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi><mo>=</mo><mn>1200</mn><msup><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mspace width="negativethinmathspace"></mspace><mi>log</mi><mo></mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle ^{\sqrt[{1200}]{2}}\!\log r=1200\,^{2}\!\log r}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82119fb5a559f76705c1639cb63b2fb210e081a4" style="border: 0px; display: inline-block; height: 3.676ex; vertical-align: -0.671ex; width: 22.154ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 16{\tfrac {2}{3}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>16</mn><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mn>2</mn><mn>3</mn></mfrac></mstyle></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 16{\tfrac {2}{3}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a14ffb45717ec74dc340583a93d6a788f6179382" style="border: 0px; display: inline-block; height: 3.676ex; vertical-align: -1.338ex; width: 3.983ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 100}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>100</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 100}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0572cd017c6d7936a12737c9d614a2f801f94a36" style="border: 0px; display: inline-block; height: 2.176ex; vertical-align: -0.338ex; width: 3.487ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \approx 386,31}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>≈</mo><mn>386</mn><mo>,</mo><mn>31</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \approx 386,31}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cf8005a33b653389a975c7888dd178d9a01ca36" style="border: 0px; display: inline-block; height: 2.509ex; vertical-align: -0.671ex; width: 9.3ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 400}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>400</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 400}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8540670f7baa60a08a5dd4b12916c16fe6faf200" style="border: 0px; display: inline-block; height: 2.176ex; vertical-align: -0.338ex; width: 3.487ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 600}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>600</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 600}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ed5fbc94ba594303754ec8efd3d552547a93043" style="border: 0px; display: inline-block; height: 2.176ex; vertical-align: -0.338ex; width: 3.487ex;" /></span></td><td style="border: 1px solid rgb(162, 169, 177); padding: 0.2em 0.4em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 1200}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>1200</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 1200}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/973054497debca94837d3a844349fe9221727dbd" style="border: 0px; display: inline-block; height: 2.176ex; vertical-align: -0.338ex; width: 4.65ex;" /></span></td></tr></tbody></table><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Penerapannya_dalam_teori_bilangan">Penerapannya dalam teori bilangan</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=33" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Penerapannya dalam teori bilangan">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=33" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Penerapannya dalam teori bilangan">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;"><a href="https://id.wikipedia.org/wiki/Logaritma_alami" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma alami">Logaritma alami</a> sangat berkaitan dengan salah satu topik dalam <a href="https://id.wikipedia.org/wiki/Teori_bilangan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teori bilangan">teori bilangan</a>, yaitu <a href="https://id.wikipedia.org/wiki/Fungsi_pencacahan_bilangan_prima" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi pencacahan bilangan prima">menghitung bilangan prima</a>. Untuk setiap <a href="https://id.wikipedia.org/wiki/Bilangan_bulat" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan bulat">bilangan bulat</a> <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>, jumlah <a href="https://id.wikipedia.org/wiki/Bilangan_prima" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan prima">bilangan prima</a> kurang dari sama dengan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> dinyatakan sebagai <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><a href="https://id.wikipedia.org/wiki/Fungsi_pencacahan_bilangan_prima" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi pencacahan bilangan prima"><span class="texhtml" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">π</span>(<i>x</i>)</a></span>. <a href="https://id.wikipedia.org/wiki/Teorema_bilangan_prima" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teorema bilangan prima">Teorema bilangan prima</a> mengatakan bahwa <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><span class="texhtml" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">π</span>(<i>x</i>)</span> kira-kira sama dengan</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\frac {x}{\ln(x)}},}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo></mrow></mfrac></mrow><mo>,</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\frac {x}{\ln(x)}},}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e7c35556de976b4896475a163d924bb9f3d83eb" style="border: 0px; display: inline-block; height: 5.509ex; vertical-align: -2.671ex; width: 6.561ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">yang berarti bahwa fungsi pencacahan bilangan prima kira-kira sama dengan perbandingan dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><span class="texhtml" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">π</span>(<i>x</i>)</span> dan pecahan yang mendekati 1 ketika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> menuju ke takhingga.<sup class="reference" id="cite_ref-95" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-95" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[90]</a></sup> Akibatnya, peluang dari bilangan yang dipilih secara acak di antara 1 dan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> adalah bilangan prima <a href="https://id.wikipedia.org/wiki/Kesebandingan_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kesebandingan (matematika)">berbanding</a> terbalik dengan jumlah digit desimal <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>. Pendekatan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><span class="texhtml" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">π</span>(<i>x</i>)</span> yang lebih baik merupakan <a href="https://id.wikipedia.org/wiki/Fungsi_integral_logaritmik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi integral logaritmik">fungsi integral Euler</a> <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">Li(<i>x</i>)</span>, yang didefinisikan sebagai</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \mathrm {Li} (x)=\int _{2}^{x}{\frac {1}{\ln(t)}}\,dt.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">L</mi><mi mathvariant="normal">i</mi></mrow><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∫</mo><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msubsup><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mrow><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo></mrow></mfrac></mrow><mspace width="thinmathspace"></mspace><mi>�</mi><mi>�</mi><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \mathrm {Li} (x)=\int _{2}^{x}{\frac {1}{\ln(t)}}\,dt.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da577950b8b4c4ef726a3065afcdafa378dbc3fb" style="border: 0px; display: inline-block; height: 6.176ex; vertical-align: -2.671ex; width: 20.875ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;"><a href="https://id.wikipedia.org/wiki/Hipotesis_Riemann" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Hipotesis Riemann">Hipotesis Riemann</a>, yang merupakan salah satu <a href="https://id.wikipedia.org/wiki/Konjektur" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Konjektur">konjektur</a> matemtika terbuka yang paling terlama, dapat dinyatakan dalam bentuk perbandingan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><span class="texhtml" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">π</span>(<i>x</i>)</span> dan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">Li(<i>x</i>)</span>.<sup class="reference" id="cite_ref-96" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-96" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[91]</a></sup> <a href="https://id.wikipedia.org/wiki/Teorema_Erd%C5%91s%E2%80%93Kac" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teorema Erdős–Kac">Teorema Erdős–Kac</a> mengatakan bahwa jumlah <a href="https://id.wikipedia.org/wiki/Bilangan_prima#Faktorisasi_unik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan prima">faktor bilangan prima</a> yang berbeda juga melibatkan <a href="https://id.wikipedia.org/wiki/Logaritma_alami" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma alami">logaritma alami</a>.</p><p style="margin: 0.5em 0px 1em;">Logaritma dari <i>n</i> <a href="https://id.wikipedia.org/wiki/Faktorial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Faktorial">faktorial</a>, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>n</i>! = 1 · 2 · ... · <i>n</i></span>, dirumuskan sebagai</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \ln(n!)=\ln(1)+\ln(2)+\cdots +\ln(n).}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo>!</mo><mo stretchy="false">)</mo><mo>=</mo><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mo>+</mo><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo>+</mo><mo>⋯</mo><mo>+</mo><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \ln(n!)=\ln(1)+\ln(2)+\cdots +\ln(n).}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/207af1498eca9a74c5e19ecab897d915d1052c95" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.838ex; width: 35.746ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Rumus di atas dapat dipakai utnuk memperoleh sebuah hampiran dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>n</i>!</span> untuk setiap bilangan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">n</span> yang lebih besar, yaitu <a class="new" href="https://id.wikipedia.org/w/index.php?title=Rumus_Stirling&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Rumus Stirling (halaman belum tersedia)">rumus Stirling</a>.<sup class="reference" id="cite_ref-97" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-97" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[92]</a></sup></p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Perumuman">Perumuman</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=34" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Perumuman">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=34" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Perumuman">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Logaritma_kompleks">Logaritma kompleks</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=35" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Logaritma kompleks">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=35" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Logaritma kompleks">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><div class="hatnote navigation-not-searchable" role="note" style="font-style: italic; margin-bottom: 0.5em; padding-left: 1.6em;">Artikel utama: <a class="new" href="https://id.wikipedia.org/w/index.php?title=Logaritma_kompleks&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma kompleks (halaman belum tersedia)">Logaritma kompleks</a></div><p style="margin: 0.5em 0px 1em;">Semua <a href="https://id.wikipedia.org/wiki/Bilangan_kompleks" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan kompleks">bilangan kompleks</a> <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">a</span> yang menyelesaikan persamaan</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle e^{a}=z}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>=</mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle e^{a}=z}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7dc3322ef38b06276c3bee59d656769b6edf531f" style="border: 0px; display: inline-block; height: 2.343ex; vertical-align: -0.338ex; width: 6.372ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">disebut <i>logaritma kompleks</i> dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span>, ketika <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> (dianggap sebagai) bilangan kompleks. Bilangan kompleks biasanya dinyatakan sebagai <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>z = x + iy</i></span>, dengan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> dan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">y</span> adalah bilangan real dan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">i</span> adalah <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Satuan_imajiner" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Satuan imajiner">satuan imajiner</a> (satuan yang dikuadratkan memberikan nilai −1). Bilangan kompleks dapat divisualisasikan melalui sebuah titik dalam <a href="https://id.wikipedia.org/wiki/Bidang_kompleks" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bidang kompleks">bidang kompleks</a>, seperti yang diperlihatkan pada gambar berikut. <a href="https://id.wikipedia.org/wiki/Bilangan_kompleks#Bidang_kompleks_polar" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan kompleks">Bentuk polar</a> menulis bilangan kompleks tak-nol <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> melalui titik <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Nilai_mutlak" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Nilai mutlak">nilai mutlak</a>, yang berarti jarak yang berupa bilangan bernilai real dan positif <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">r</span> sama dengan titik <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> ke <a href="https://id.wikipedia.org/wiki/Titik_nol" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Titik nol">titik asalnya</a>. Bentuk polar juga menulis sebuah sudut antara bilangan real pada sumbu-<span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">Re</span> (yakni sumbu-<span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span>) <i> </i><span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">Re</span> dan garis yang melalui titik asal dan titik <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span>. Sudut tersebut disebut sebagai <a class="new" href="https://id.wikipedia.org/w/index.php?title=Argumen_(bilangan_kompleks)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Argumen (bilangan kompleks) (halaman belum tersedia)">argumen</a> dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span>.</p><figure class="mw-default-size" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; display: table; float: right; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Complex_number_illustration_multiple_arguments.svg" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img alt="Sebuah ilustrasi mengenai bentuk polar: sebuah titik yang dijelaskan melalui sebuah panah atau secara ekuivalen melalui panjang dan sudutnya ke sumbu-x." class="mw-file-element" data-file-height="217" data-file-width="204" decoding="async" height="234" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/83/Complex_number_illustration_multiple_arguments.svg/220px-Complex_number_illustration_multiple_arguments.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Complex_number_illustration_multiple_arguments.svg/330px-Complex_number_illustration_multiple_arguments.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Complex_number_illustration_multiple_arguments.svg/440px-Complex_number_illustration_multiple_arguments.svg.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="220" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Bentuk polar dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>z = x + iy</i></span>. <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">φ</span> dan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">φ'</span> adalah argumen dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span>.</figcaption></figure><p style="margin: 0.5em 0px 1em;">Nilai mutlak <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">r</span> dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> dinyatakan sebagai</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \textstyle r={\sqrt {x^{2}+y^{2}}}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="false" scriptlevel="0"><mi>�</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><msqrt><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></msqrt></mrow><mo>.</mo></mstyle></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \textstyle r={\sqrt {x^{2}+y^{2}}}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c0606ea41983c11ed8e73fc1507ce58ad316ef0" style="border: 0px; display: inline-block; height: 3.509ex; vertical-align: -1.005ex; width: 14.557ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Dengan menggunakan pandangan geometris pada fungsi <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Sinus_(trigonometri)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Sinus (trigonometri)">sinus</a> dan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Kosinus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kosinus">kosinus</a> beserta periodisitasnya dalam <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">2<span class="texhtml" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">π</span></span>, setiap bilangan kompleks <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> dapat dinyatakan sebagai</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle z=x+iy=r(\cos \varphi +i\sin \varphi )=r(\cos(\varphi +2k\pi )+i\sin(\varphi +2k\pi )),}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>=</mo><mi>�</mi><mo>+</mo><mi>�</mi><mi>�</mi><mo>=</mo><mi>�</mi><mo stretchy="false">(</mo><mi>cos</mi><mo></mo><mi>�</mi><mo>+</mo><mi>�</mi><mi>sin</mi><mo></mo><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><mi>�</mi><mo stretchy="false">(</mo><mi>cos</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo>+</mo><mn>2</mn><mi>�</mi><mi>�</mi><mo stretchy="false">)</mo><mo>+</mo><mi>�</mi><mi>sin</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo>+</mo><mn>2</mn><mi>�</mi><mi>�</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>,</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle z=x+iy=r(\cos \varphi +i\sin \varphi )=r(\cos(\varphi +2k\pi )+i\sin(\varphi +2k\pi )),}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d0927f8e12e74d5bc6aa939122acb09bd8a4c84" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.838ex; width: 66.433ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">untuk setiap bilangan bulat <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">k</span>. Nyatanya, argumen dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> tidak dijelaskan secara unik, yakni: bilangan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">φ</span> dan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>φ'</i> = <i>φ</i> + 2<i>k</i><span class="texhtml" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">π</span></span> adalah argumen valid dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> untuk semua bilangan bulat <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">k</span>, karena menambahkan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">2<i>k</i><span class="texhtml" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">π</span></span> <a href="https://id.wikipedia.org/wiki/Radian" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Radian">radian</a> atau <i>k</i>⋅360°<sup class="reference" id="cite_ref-98" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-98" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[nb 6]</a></sup> ke bilangan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">φ</span> berpadanan dengan "lilitan" di sekitar titik asal yang berputar berlawanan arah jarum jam sebanyak <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">k</span> <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Putaran_(geometri)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Putaran (geometri)">putaran</a>. Hasil bilangan kompleks selalu <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span>, seperti yang diilustrasikan pada gambar untuk <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>k</i> = 1</span>. Setidaknya ada salah satu dari argumen <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> yang mungkin disebut sebagai <i>argumen prinsip</i>, yang dilambangkan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">Arg(<i>z</i>)</span>, dipilih dengan memerlukan putaran <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">φ</span> di <a href="https://id.wikipedia.org/wiki/Selang_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Selang (matematika)">selang</a> <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">(−π, π]</span><sup class="reference" id="cite_ref-99" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-99" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[93]</a></sup> atau <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">[0, 2<span class="texhtml" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">π</span>)</span>.<sup class="reference" id="cite_ref-100" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-100" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[94]</a></sup> Daerah-daerah tersebut, dengan argumen <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> ditentukan sekali disebut <a class="new" href="https://id.wikipedia.org/w/index.php?title=Cabang_prinsip&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Cabang prinsip (halaman belum tersedia)"><i>cabang</i></a> dari fungsi argumen.</p><p style="margin: 0.5em 0px 1em;"><a href="https://id.wikipedia.org/wiki/Rumus_Euler" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Rumus Euler">Rumus Euler</a> mengaitkan <a href="https://id.wikipedia.org/wiki/Fungsi_trigonometri" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi trigonometri">fungsi trigonometri</a> <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Sinus_(trigonometri)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Sinus (trigonometri)">sinus</a> dan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Kosinus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kosinus">kosinus</a> dengan <a href="https://id.wikipedia.org/wiki/Rumus_Euler" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Rumus Euler">eksponensial kompleks</a>:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle e^{i\varphi }=\cos \varphi +i\sin \varphi .}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mi>�</mi></mrow></msup><mo>=</mo><mi>cos</mi><mo></mo><mi>�</mi><mo>+</mo><mi>�</mi><mi>sin</mi><mo></mo><mi>�</mi><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle e^{i\varphi }=\cos \varphi +i\sin \varphi .}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/396158ab1664889849843ce26a324ed8dbbf841e" style="border: 0px; display: inline-block; height: 3.176ex; vertical-align: -0.838ex; width: 20.515ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Dengan menggunakan rumus di atas, dan periodisitasnya lagi, maka berlaku identitas berikut:<sup class="reference" id="cite_ref-101" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-101" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[95]</a></sup></p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\begin{array}{lll}z&=&r\left(\cos \varphi +i\sin \varphi \right)\\&=&r\left(\cos(\varphi +2k\pi )+i\sin(\varphi +2k\pi )\right)\\&=&re^{i(\varphi +2k\pi )}\\&=&e^{\ln(r)}e^{i(\varphi +2k\pi )}\\&=&e^{\ln(r)+i(\varphi +2k\pi )}=e^{a_{k}},\end{array}}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mtable columnalign="left left left" columnspacing="1em" rowspacing="4pt"><mtr><mtd><mi>�</mi></mtd><mtd><mo>=</mo></mtd><mtd><mi>�</mi><mrow><mo>(</mo><mrow><mi>cos</mi><mo></mo><mi>�</mi><mo>+</mo><mi>�</mi><mi>sin</mi><mo></mo><mi>�</mi></mrow><mo>)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo></mtd><mtd><mi>�</mi><mrow><mo>(</mo><mrow><mi>cos</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo>+</mo><mn>2</mn><mi>�</mi><mi>�</mi><mo stretchy="false">)</mo><mo>+</mo><mi>�</mi><mi>sin</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo>+</mo><mn>2</mn><mi>�</mi><mi>�</mi><mo stretchy="false">)</mo></mrow><mo>)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo></mtd><mtd><mi>�</mi><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo>+</mo><mn>2</mn><mi>�</mi><mi>�</mi><mo stretchy="false">)</mo></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo></mtd><mtd><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo></mrow></msup><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo>+</mo><mn>2</mn><mi>�</mi><mi>�</mi><mo stretchy="false">)</mo></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo></mtd><mtd><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>+</mo><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo>+</mo><mn>2</mn><mi>�</mi><mi>�</mi><mo stretchy="false">)</mo></mrow></msup><mo>=</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub></mrow></msup><mo>,</mo></mtd></mtr></mtable></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\begin{array}{lll}z&=&r\left(\cos \varphi +i\sin \varphi \right)\\&=&r\left(\cos(\varphi +2k\pi )+i\sin(\varphi +2k\pi )\right)\\&=&re^{i(\varphi +2k\pi )}\\&=&e^{\ln(r)}e^{i(\varphi +2k\pi )}\\&=&e^{\ln(r)+i(\varphi +2k\pi )}=e^{a_{k}},\end{array}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88e5cade11df0130b973bedde60077ac9569ef7c" style="border: 0px; display: inline-block; height: 16.843ex; vertical-align: -7.838ex; width: 41.286ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">dengan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(<i>r</i>)</span> adalah fungsi logaritma real tunggal, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>a</i><sub style="font-size: 13.216px; line-height: 1;"><i>k</i></sub></span> menyatakan logaritma kompleks dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span>, dan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">k</span> bilangan bulat sembarang. Karena itu, logaritma kompleks dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span>, yang semua bilangan kompleks <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>a</i><sub style="font-size: 13.216px; line-height: 1;"><i>k</i></sub></span> untuk <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">e</span> pangkat <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>a</i><sub style="font-size: 13.216px; line-height: 1;"><i>k</i></sub></span> sama dengan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span>, mempunyai tak berhingga banyaknya nilai</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle a_{k}=\ln(r)+i(\varphi +2k\pi ),\quad }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo>=</mo><mi>ln</mi><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>+</mo><mi>�</mi><mo stretchy="false">(</mo><mi>�</mi><mo>+</mo><mn>2</mn><mi>�</mi><mi>�</mi><mo stretchy="false">)</mo><mo>,</mo><mspace width="1em"></mspace></mstyle></mrow></semantics></math></span><img alt="{\displaystyle a_{k}=\ln(r)+i(\varphi +2k\pi ),\quad }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/acd46f348b53d1c0fcf39cd11e990617844255c7" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.838ex; width: 26.702ex;" /></span> untuk bilangan bulat sembarang <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">k</span>.</dd></dl><figure class="mw-default-size mw-halign-left" style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: left; display: table; float: left; line-height: 0; margin: 0.5em 1.4em 1.3em 0px; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Complex_log_domain.svg" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img alt="A density plot. In the middle there is a black point, at the negative axis the hue jumps sharply and evolves smoothly otherwise." class="mw-file-element" data-file-height="426" data-file-width="569" decoding="async" height="165" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/af/Complex_log_domain.svg/220px-Complex_log_domain.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Complex_log_domain.svg/330px-Complex_log_domain.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/af/Complex_log_domain.svg/440px-Complex_log_domain.svg.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="220" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Cabang prinsip (-<span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">π</span>, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">π</span>) dari prinsip logaritma kompleks, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">Log(<i>z</i>)</span>. Titik berwarna hitam di <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>z</i> = 1</span> berpadanan dengan nilai titik nol dan warna yang lebih cerah mengacu pada nilai mutlak lebih besar. <a href="https://id.wikipedia.org/wiki/Rona" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Rona">Rona</a> dari warna mengkodekan argumen dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.6037px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">Log(<i>z</i>)</span>.</figcaption></figure><p style="margin: 0.5em 0px 1em;">Dengan mengambil <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">k</span> sehingga <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>φ</i> + 2<i>k</i><span class="texhtml" style="font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1;">π</span></span> ada di dalam selang yang ditentukan untuk argumen prinsip, maka <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>a</i><sub style="font-size: 13.216px; line-height: 1;"><i>k</i></sub></span> disebut <i>nilai prinsip</i> dari logaritma, dinotasikan sebagai <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">Log(<i>z</i>)</span>. Argumen prinsip setiap bilangan real positif <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> bernilai 0, jadi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">Log(<i>x</i>)</span> adalah sebuah bilangan real yang sama dengan logaritma (alami). Akan tetapi, rumus logaritma tentang darab dan perpangkatan bilangan di atas <a href="https://id.wikipedia.org/wiki/Eksponensiasi#Kegagalan_identitas_perpangkatan_dan_logaritma" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Eksponensiasi">tidak memberikan perumuman</a> terkait nilai prinsip dari logaritma kompleks.<sup class="reference" id="cite_ref-102" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-102" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[96]</a></sup></p><p style="margin: 0.5em 0px 1em;">Ilustrasi tersebut menggambarkan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">Log(<i>z</i>)</span>, membatasi argumen <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span> dengan interval <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">(−π, π]</span>. Cara memadankan cabang dari logaritma kompleks mempunyai ketakkontinuan di sepanjang sumbu-<span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> real negatif, seperti yang dapat dilihat pada lompatan hue di gambar. Saat melintasi batas, ketakkontinuan tersebut dimulai dari lompatan hingga batas lain yang ada di cabang yang sama, dalam artian bahwa tiada perubahan dengan nilai-<span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">k</span> dari cabang tetangga kontinu yang berpadanan. Lokus tersebut dinamakan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Potongan_cabang&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Potongan cabang (halaman belum tersedia)">potongan cabang</a>. Dengan menghapus perbatasan argumen, maka relasi "argumen dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span>" dan "logaritma dari <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">z</span>" menjadi <a class="new" href="https://id.wikipedia.org/w/index.php?title=Fungsi_bernilai_banyak&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi bernilai banyak (halaman belum tersedia)">fungsi bernilai banyak</a>.</p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Kebalikan_dari_fungsi_eksponensial_lainnya">Kebalikan dari fungsi eksponensial lainnya</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=36" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Kebalikan dari fungsi eksponensial lainnya">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=36" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Kebalikan dari fungsi eksponensial lainnya">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;">Eksponensiasi muncul dalam cabang matematika dan fungsi inversnya seringkali mengacu pada logaritma. Sebagai contoh, <a class="new" href="https://id.wikipedia.org/w/index.php?title=Logaritma_matriks&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma matriks (halaman belum tersedia)">logaritma matriks</a> merupakan fungsi invers (bernilai banyak) dari <a class="new" href="https://id.wikipedia.org/w/index.php?title=Eksponensial_matriks&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Eksponensial matriks (halaman belum tersedia)">eksponensial matriks</a>.<sup class="reference" id="cite_ref-103" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-103" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[97]</a></sup> Contohnya lain seperti <a class="new" href="https://id.wikipedia.org/w/index.php?title=Fungsi_logaritma_p-adic&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi logaritma p-adic (halaman belum tersedia)">fungsi logaritma <i>p</i>-adic</a>, fungsi invers dari <a class="new" href="https://id.wikipedia.org/w/index.php?title=Fungsi_eksponensial_p-adic&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi eksponensial p-adic (halaman belum tersedia)">fungsi eksponensial <i>p</i>-adic</a>. Kedua fungsi tersebut didefinisikan melalui deret Taylor yang analog dengan kasus bilangan real.<sup class="reference" id="cite_ref-104" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-104" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[98]</a></sup> Dalam konteks <a href="https://id.wikipedia.org/wiki/Geometri_diferensial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Geometri diferensial">geometri diferensial</a>, <a class="new" href="https://id.wikipedia.org/w/index.php?title=Peta_eksponensial_(geometri_Riemann)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Peta eksponensial (geometri Riemann) (halaman belum tersedia)">peta eksponensial</a> memetakan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Ruang_garis_singgung&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Ruang garis singgung (halaman belum tersedia)">ruang garis singgung</a> di sebuah titik <a href="https://id.wikipedia.org/wiki/Lipatan_terdiferensialkan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Lipatan terdiferensialkan">lipatan</a> ke <a href="https://id.wikipedia.org/wiki/Lingkungan_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Lingkungan (matematika)">lingkungan</a> titik tersebut. Kebalikannya juga disebut peta logaritma.<sup class="reference" id="cite_ref-105" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-105" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[99]</a></sup></p><p style="margin: 0.5em 0px 1em;">Dalam konteks <a href="https://id.wikipedia.org/wiki/Grup_hingga" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Grup hingga">grup hingga</a>, eksponensiasi dinyatakan dengan mengalikan satu anggota grup <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">b</span> dengan dirinya secara berulang. <a href="https://id.wikipedia.org/wiki/Logaritma_diskret" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma diskret">Logaritma diskret</a> merupakan bilangan bulat <i><span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">n</span></i> yang menyelesaikan persamaan</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle b^{n}=x,}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>=</mo><mi>�</mi><mo>,</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle b^{n}=x,}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f90e5e0851759d0490e085cf1888338465384143" style="border: 0px; display: inline-block; height: 2.676ex; vertical-align: -0.671ex; width: 7.291ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">dengan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">x</span> adalah anggota dari grup. Mengerjakan solusi eksponensiasi dapat dilakukan dengan efisien, namun logaritma diskret dipercayai bahwa sangat sulit untuk menghitungnya dalam beberapa grup. Asimetri dari grup tersebut mempunyai penerapan penting dalam <a href="https://id.wikipedia.org/wiki/Kriptografi_kunci_publik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kriptografi kunci publik">kriptografi kunci publik</a>, contohnya seperti <a href="https://id.wikipedia.org/wiki/Pertukaran_kunci_Diffie%E2%80%93Hellman" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Pertukaran kunci Diffie–Hellman">pertukaran kunci Diffie–Hellman</a>, sebuah pertukaran kunci sehari-hari yang memungkinkan pertukaran kunci <a href="https://id.wikipedia.org/wiki/Kriptografi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kriptografi">kriptografi</a> terhadap saluran informasi yang tidak diamankan.<sup class="reference" id="cite_ref-106" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-106" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[100]</a></sup> <a class="new" href="https://id.wikipedia.org/w/index.php?title=Logaritma_Zech&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma Zech (halaman belum tersedia)">Logaritma Zech</a> berkaitan dengan logaritma diskret dalam grup perkalian anggota taknol dari <a href="https://id.wikipedia.org/wiki/Medan_hingga" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Medan hingga">medan hingga</a>.<sup class="reference" id="cite_ref-107" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-107" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[101]</a></sup></p><p style="margin: 0.5em 0px 1em;"><span id="double_logarithm"></span>Adapun fungsi invers berupa logaritma lainnya. Fungsi tersebut di antaranya: <i>logaritma ganda</i> <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ln(ln(<i>x</i>))</span> yang merupakan kebalikan dari <a href="https://id.wikipedia.org/wiki/Fungsi_eksponensial_ganda" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi eksponensial ganda">fungsi eksponensial ganda</a>, <i><a class="new" href="https://id.wikipedia.org/w/index.php?title=Superlogaritma&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Superlogaritma (halaman belum tersedia)">superlogaritma</a></i> yang merupakan kebalikan dari <a href="https://id.wikipedia.org/wiki/Tetrasi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Tetrasi">tetrasi</a>, <a href="https://id.wikipedia.org/wiki/Fungsi_Lambert_W" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi Lambert W">fungsi Lambert W</a> yang merupakan kebalikan dari fungsi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>f</i>(<i>w</i>) = <i>we<sup style="font-size: 13.216px; line-height: 1;">w</sup></i></span>,<sup class="reference" id="cite_ref-108" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-108" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[102]</a></sup> dan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Logit&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Logit (halaman belum tersedia)">logit</a> yang merupakan kebalikan dari <a class="new" href="https://id.wikipedia.org/w/index.php?title=Fungsi_logistik&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi logistik (halaman belum tersedia)">fungsi logistik</a>.<sup class="reference" id="cite_ref-109" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-109" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[103]</a></sup></p><h3 style="color: black; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Konsep_yang_berkaitan">Konsep yang berkaitan</span><span class="mw-editsection" style="font-size: small; font-weight: normal; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Logaritma&veaction=edit&section=37" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Konsep yang berkaitan">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Logaritma&action=edit&section=37" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Konsep yang berkaitan">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h3><p style="margin: 0.5em 0px 1em;">Berdasarkan sudut pandang <a href="https://id.wikipedia.org/wiki/Teori_grup" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teori grup">teori grup</a>, identitas <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">log(<i>cd</i>) = log(<i>c</i>) + log(<i>d</i>)</span> menyatakan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Isomorfisme_grup&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Isomorfisme grup (halaman belum tersedia)">isomorfisme grup</a> antara bilangan <a href="https://id.wikipedia.org/wiki/Bilangan_riil" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan riil">riil</a> positif terhadap perkalian bilangan riil positif terhadap penambahan. Fungsi logaritmik hanya isomorfisme kontinu antara grup.<sup class="reference" id="cite_ref-110" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-110" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[104]</a></sup> Berdasarkan pengertian isomorfisme tersebut, <a class="new" href="https://id.wikipedia.org/w/index.php?title=Ukuran_Haar&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Ukuran Haar (halaman belum tersedia)">ukuran Haar</a> (<a class="new" href="https://id.wikipedia.org/w/index.php?title=Ukuran_Lebesgue&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Ukuran Lebesgue (halaman belum tersedia)">ukuran Lebesgue</a>) <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>dx</i></span> pada riil berpadanan dengan ukuran Haar <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><span class="sfrac nowrap" style="display: inline-block; font-size: 14.042px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;"><i>dx</i></span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;"><i>x</i></span></span></span> pada bilangan real positif.<sup class="reference" id="cite_ref-111" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-111" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[105]</a></sup> Bilangan riil taknegatif tidak hanya terhadap operasi perkalian, namun juga terhadap operasi penambahan, dan bilangan riil taknegatif membentuk <a href="https://id.wikipedia.org/wiki/Semigelanggang" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Semigelanggang">semigelanggang</a>, yang disebut sebagai <a href="https://id.wikipedia.org/wiki/Semigelanggang#Probabilitas_semigelanggang" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Semigelanggang">semigelanggang probabilitas</a>, bahkan membentuk <a href="https://id.wikipedia.org/wiki/Semigelanggang" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Semigelanggang">semigelanggang</a>. Maka logaritma yang mengambil perkalian dengan penambahan (perkalian logaritma), dan mengambil penambahan dengan penambahan logaritma, memberikan <a href="https://id.wikipedia.org/wiki/Isomorfisme" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Isomorfisme">isomorfisme</a> semigelanggang di antara semigelanggang probabilitas dan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Semigelanggang_logaritma&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Semigelanggang logaritma (halaman belum tersedia)">semigelanggang logaritma</a>.</p><p style="margin: 0.5em 0px 1em;">Konsep ini juga terdapat di dalam <a href="https://id.wikipedia.org/wiki/Analisis_kompleks" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Analisis kompleks">analisis kompleks</a> dan <a href="https://id.wikipedia.org/wiki/Geometri_aljabar" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Geometri aljabar">geometri aljabar</a>, yang <a class="new" href="https://id.wikipedia.org/w/index.php?title=Bentuk_logaritmik&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Bentuk logaritmik (halaman belum tersedia)">logaritmik satu bentuk </a><span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>df</i>/<i>f</i></span> adalah <a class="new" href="https://id.wikipedia.org/w/index.php?title=Bentuk_diferensial&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Bentuk diferensial (halaman belum tersedia)">bentuk diferensial</a> dengan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Pole_(analisis_kompleks)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Pole (analisis kompleks) (halaman belum tersedia)">pole</a> logaritmik.<sup class="reference" id="cite_ref-112" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-112" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[106]</a></sup></p><p style="margin: 0.5em 0px 1em;">Selain itu, terdapat <a class="new" href="https://id.wikipedia.org/w/index.php?title=Polilogaritma&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Polilogaritma (halaman belum tersedia)">polilogaritma</a>, sebuah fungsi yang didefinisikan sebagai</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \operatorname {Li} _{s}(z)=\sum _{k=1}^{\infty }{z^{k} \over k^{s}}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>Li</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msub><mo></mo><mo stretchy="false">(</mo><mi>�</mi><mo stretchy="false">)</mo><mo>=</mo><munderover><mo>∑</mo><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mo>=</mo><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><mrow class="MJX-TeXAtom-ORD"><mfrac><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mfrac></mrow><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \operatorname {Li} _{s}(z)=\sum _{k=1}^{\infty }{z^{k} \over k^{s}}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c16a216f9168ba23df2d07ceb32c6929a70c4e1b" style="border: 0px; display: inline-block; height: 6.843ex; vertical-align: -3.005ex; width: 16.538ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Fungsi ini mempunyai kaitan dengan <a href="https://id.wikipedia.org/wiki/Logaritma_alami" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="">logaritma alami</a> dengan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">Li<sub style="font-size: 13.216px; line-height: 1;">1</sub> (<i>z</i>) = −ln(1 − <i>z</i>)</span>. Terlebih lagi, ketika <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>z</i> = 1</span>, nilai dari <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">Li<sub style="font-size: 13.216px; line-height: 1;"><i>s</i></sub> (1)</span> sama dengan <a href="https://id.wikipedia.org/wiki/Fungsi_zeta_Riemann" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi zeta Riemann">fungsi zeta Riemann</a>, yang dinyatakan sebagai <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">ζ(<i>s</i>)</span>.<sup class="reference" id="cite_ref-113" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Logaritma#cite_note-113" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[107]</a></sup></p></div></div></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8185710560472973854.post-33305522590345894032024-01-29T13:39:00.005+07:002024-01-29T13:39:37.482+07:00Eksponensial<p> </p><header class="mw-body-header vector-page-titlebar" style="align-items: center; background-color: white; box-shadow: none; color: #202122; display: flex; flex-wrap: nowrap; font-family: sans-serif; font-size: 16px; grid-area: titlebar / titlebar / titlebar / titlebar; justify-content: flex-end; position: relative;"><h1 class="firstHeading mw-first-heading" id="firstHeading" style="border: 0px; color: black; flex-grow: 1; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-size: 1.8em; font-weight: normal; line-height: 1.375; margin: 0px; overflow-wrap: break-word; overflow: hidden; padding: 0px;"><span class="mw-page-title-main">Fungsi eksponensial</span></h1><div class="vector-dropdown mw-portlet mw-portlet-lang" id="p-lang-btn" style="box-sizing: border-box; flex-shrink: 0; float: right; margin-right: -12px; position: relative;"><input aria-haspopup="true" aria-label="Pergi ke artikel dalam bahasa lain. 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margin-top: 8px;">Dari Wikipedia bahasa Indonesia, ensiklopedia bebas</div></div><div id="contentSub" style="color: #54595d; font-size: 0.875rem; margin: 8px 0px 0px; width: auto;"><div id="mw-content-subtitle"></div></div><div class="mw-body-content" id="mw-content-text" style="margin-top: 16px;"><div class="mw-content-ltr mw-parser-output" dir="ltr" lang="id"><table class="box-Tanpa_referensi plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation" style="background-color: #fbfbfb; border-color: rgb(162, 169, 177) rgb(162, 169, 177) rgb(162, 169, 177) rgb(242, 133, 0); border-image: initial; border-style: solid; border-width: 1px 1px 1px 10px; font-size: 14px; margin: 0px 94.7969px;"><tbody><tr><td class="mbox-image" style="border: none; padding: 2px 0px 2px 0.5em; text-align: center;"><div class="mbox-image-div" style="width: 52px;"><span typeof="mw:File"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Question_book-new.svg" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;"><img class="mw-file-element" data-file-height="399" data-file-width="512" decoding="async" height="39" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" style="border: 0px; vertical-align: middle;" width="50" /></a></span></div></td><td class="mbox-text" style="border: none; padding: 0.25em 0.5em; width: 668.406px;"><div class="mbox-text-span">Artikel ini tidak <b>memiliki <a href="https://id.wikipedia.org/wiki/Wikipedia:Kutip_sumber_tulisan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Wikipedia:Kutip sumber tulisan">referensi</a> atau <a href="https://id.wikipedia.org/wiki/Wikipedia:Sumber_tepercaya" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Wikipedia:Sumber tepercaya">sumber tepercaya</a> sehingga isinya tidak bisa <a href="https://id.wikipedia.org/wiki/Wikipedia:Pemastian" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Wikipedia:Pemastian">dipastikan</a></b>.<span class="hide-when-compact"> Tolong bantu <span class="plainlinks"><a class="external text" href="https://id.wikipedia.org/w/index.php?title=Fungsi_eksponensial&action=edit" style="background: none !important; color: #3366cc; overflow-wrap: break-word; padding: 0px !important; text-decoration-line: none;">perbaiki artikel ini</a></span> dengan menambahkan referensi yang layak. Tulisan tanpa sumber dapat dipertanyakan dan dihapus sewaktu-waktu.<br /><small style="font-size: 11.9px;"><span class="plainlinks"><i>Cari sumber:</i> <a class="external text" href="https://google.com/search?as_eq=wikipedia&q=%22Fungsi+eksponensial%22&num=50" rel="nofollow" style="background: none !important; color: #3366cc; overflow-wrap: break-word; padding: 0px !important; text-decoration-line: none;">"Fungsi eksponensial"</a> – <a class="external text" href="https://google.com/search?q=%22Fungsi+eksponensial%22&tbm=nws" rel="nofollow" style="background: none !important; color: #3366cc; overflow-wrap: break-word; padding: 0px !important; text-decoration-line: none;">berita</a> <b>·</b> <a class="external text" href="https://google.com/search?&q=%22Fungsi+eksponensial%22+site:news.google.com/newspapers&source=newspapers" rel="nofollow" style="background: none !important; color: #3366cc; overflow-wrap: break-word; padding: 0px !important; text-decoration-line: none;">surat kabar</a> <b>·</b> <a class="external text" href="https://google.com/search?tbs=bks:1&q=%22Fungsi+eksponensial%22" rel="nofollow" style="background: none !important; color: #3366cc; overflow-wrap: break-word; padding: 0px !important; text-decoration-line: none;">buku</a> <b>·</b> <a class="external text" href="https://scholar.google.com/scholar?q=%22Fungsi+eksponensial%22" rel="nofollow" style="background: none !important; color: #3366cc; overflow-wrap: break-word; padding: 0px !important; text-decoration-line: none;">cendekiawan</a> <b>·</b> <a class="external text" href="http://www.jstor.org/action/doBasicSearch?Query=%22Fungsi+eksponensial%22&acc=on&wc=on" rel="nofollow" style="background: none !important; color: #3366cc; overflow-wrap: break-word; padding: 0px !important; text-decoration-line: none;">JSTOR</a></span></small></span></div></td></tr></tbody></table><table class="sidebar sidebar-collapse nomobile hlist" style="background: rgb(248, 249, 250); border-collapse: collapse; border: 1px solid rgb(170, 170, 170); clear: right; float: right; font-size: 12.32px; line-height: 1.4em; margin: 0.5em 0px 1em 1em; padding: 0.2em; text-align: center; width: 20em;"><tbody><tr><td class="sidebar-pretitle" style="line-height: 1.2em; padding: 0.4em 0.4em 0px;">Bagian dari <a href="https://id.wikipedia.org/wiki/Kategori:Konstanta_matematika" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kategori:Konstanta matematika">serial artikel</a> mengenai</td></tr><tr><th class="sidebar-title-with-pretitle" style="font-size: 16.016px; line-height: 1.2em; padding: 0.1em 0.4em;"><i><a href="https://id.wikipedia.org/wiki/E_(konstanta_matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="E (konstanta matematika)"><span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 18.8989px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">e</span></a></i></th></tr><tr><th class="sidebar-heading" style="border-bottom: 1px solid rgb(170, 170, 170); border-top: 1px solid rgb(170, 170, 170); padding: 0.1em 0.4em;"><a href="https://id.wikipedia.org/wiki/E_(konstanta_matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="E (konstanta matematika)">Artikel mengenai <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 14.5376px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">e</span></a></th></tr><tr><td class="sidebar-content" style="padding: 0px 0.5em 0.4em;"><span typeof="mw:File"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Euler%27s_formula.svg" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;"><img class="mw-file-element" data-file-height="700" data-file-width="700" decoding="async" height="180" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/71/Euler%27s_formula.svg/180px-Euler%27s_formula.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Euler%27s_formula.svg/270px-Euler%27s_formula.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/71/Euler%27s_formula.svg/360px-Euler%27s_formula.svg.png 2x" style="border: 0px; vertical-align: middle;" width="180" /></a></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 14.5376px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle 2.718\,281\,828\,459\,045\,235\,360\,287\dots }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>2.718</mn><mspace width="thinmathspace"></mspace><mn>281</mn><mspace width="thinmathspace"></mspace><mn>828</mn><mspace width="thinmathspace"></mspace><mn>459</mn><mspace width="thinmathspace"></mspace><mn>045</mn><mspace width="thinmathspace"></mspace><mn>235</mn><mspace width="thinmathspace"></mspace><mn>360</mn><mspace width="thinmathspace"></mspace><mn>287</mn><mo>…</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle 2.718\,281\,828\,459\,045\,235\,360\,287\dots }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b56cfef6431f61c7c676841131be4e27cf6761f4" style="border: 0px; 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vertical-align: top;"><span class="mw-default-size" typeof="mw:File/Frameless"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Exp.png" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;"><img class="mw-file-element" data-file-height="201" data-file-width="201" decoding="async" height="201" src="https://upload.wikimedia.org/wikipedia/commons/9/9c/Exp.png" style="border: 0px; vertical-align: middle;" width="201" /></a></span><div class="infobox-caption">Fungsi eksponensial</div></td></tr><tr><th class="infobox-header" colspan="2" style="background: rgb(224, 224, 224); padding-bottom: 0.2em; text-align: center; vertical-align: top;">Domain dan Citra</th></tr><tr><th class="infobox-label" scope="row" style="line-height: 1.2em; padding-right: 0.65em; padding-top: 0.25em; text-align: left; vertical-align: top;"><a class="mw-redirect" href="https://id.wikipedia.org/wiki/Domain" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Domain">Domain dari fungsi</a></th><td class="infobox-data" style="vertical-align: top;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 14.5376px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle (0,\infty )}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle (0,\infty )}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da17102e4ed0886686094ee531df040d2e86352a" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.838ex; width: 6.329ex;" /></span></td></tr><tr><th class="infobox-label" scope="row" style="line-height: 1.2em; padding-right: 0.65em; padding-top: 0.25em; text-align: left; vertical-align: top;"><a class="mw-redirect" href="https://id.wikipedia.org/wiki/Kodomain" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kodomain">Daerah hasil fungsi</a></th><td class="infobox-data" style="vertical-align: top;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 14.5376px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle (0,\infty )}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle (0,\infty )}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da17102e4ed0886686094ee531df040d2e86352a" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.838ex; width: 6.329ex;" /></span></td></tr><tr><th class="infobox-header" colspan="2" style="background: rgb(224, 224, 224); padding-bottom: 0.2em; text-align: center; vertical-align: top;">Nilai-nilai spesifik</th></tr><tr><th class="infobox-label" scope="row" style="line-height: 1.2em; padding-right: 0.65em; padding-top: 0.25em; text-align: left; vertical-align: top;">Nilai di 0</th><td class="infobox-data" style="vertical-align: top;">Tidak ada</td></tr><tr><th class="infobox-label" scope="row" style="line-height: 1.2em; padding-right: 0.65em; padding-top: 0.25em; text-align: left; vertical-align: top;">Nilai maksimum</th><td class="infobox-data" style="vertical-align: top;">Tidak ada</td></tr><tr><th class="infobox-label" scope="row" style="line-height: 1.2em; padding-right: 0.65em; padding-top: 0.25em; text-align: left; vertical-align: top;">Nilai minimum</th><td class="infobox-data" style="vertical-align: top;">Tidak ada</td></tr><tr><th class="infobox-label" scope="row" style="line-height: 1.2em; padding-right: 0.65em; padding-top: 0.25em; text-align: left; vertical-align: top;"><a href="https://id.wikipedia.org/wiki/Fungsi_invers" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi invers">Invers</a></th><td class="infobox-data" style="vertical-align: top;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 14.5376px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \ln x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>ln</mi><mo></mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \ln x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed172b0f5195382a3500c713941f945ad4db3898" style="border: 0px; display: inline-block; height: 2.176ex; vertical-align: -0.338ex; width: 3.656ex;" /></span> (<a class="new" href="https://id.wikipedia.org/w/index.php?title=Fungsi_logaritma_natural&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi logaritma natural (halaman belum tersedia)">fungsi logaritma natural</a>)</td></tr><tr><th class="infobox-label" scope="row" style="line-height: 1.2em; padding-right: 0.65em; padding-top: 0.25em; text-align: left; vertical-align: top;"><a href="https://id.wikipedia.org/wiki/Turunan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan">Turunan</a></th><td class="infobox-data" style="vertical-align: top;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 14.5376px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle e^{x}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle e^{x}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/841c0d168e64191c45a45e54c7e447defd17ec6a" style="border: 0px; display: inline-block; height: 2.343ex; vertical-align: -0.338ex; width: 2.256ex;" /></span></td></tr></tbody></table><p style="margin: 0.5em 0px 1em;"><b>Fungsi eksponensial</b> adalah fungsi nonaljabar atau transcendental yang tidak dapat direpresentasikan sebagai produk, jumlah, dan perbedaan variabel yang dipangkatkan ke bilangan bulat non-negatif. Fungsi eksponensial merupakan fungsi berpangkat, yang pangkatnya memiliki variabel. Biasanya, fungsi ini ditulis dengan notasi exp(<i>x</i>) atau <i>e</i><sup style="font-size: 11.2px; line-height: 1;"><i>x</i></sup>, di mana <i>e</i> adalah <a href="https://id.wikipedia.org/wiki/E_(konstanta_matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="E (konstanta matematika)">basis logaritma natural</a> yang kira-kira sama dengan 2.71828183.</p><p style="margin: 0.5em 0px 1em;">Sebagai fungsi variabel <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Bilangan_real" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan real">bilangan real</a> <i>x</i>, grafik <i>e</i><sup style="font-size: 11.2px; line-height: 1;"><i>x</i></sup> selalu positif (berada di atas sumbu <i>x</i>) dan nilainya bertambah (dilihat dari kiri ke kanan). Grafiknya tidak menyentuh sumbu <i>x</i>, tetapi mendekati sumbu tersebut secara <a class="new" href="https://id.wikipedia.org/w/index.php?title=Asimptotik&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Asimptotik (halaman belum tersedia)">asimptotik</a>. <a class="mw-disambig" href="https://id.wikipedia.org/wiki/Invers" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Invers">Invers</a> dari fungsi ini, <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Logaritma_natural" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Logaritma natural">logaritma natural</a>, atau ln(<i>x</i>), didefinisikan untuk nilai <i>x</i> yang positif.</p><p style="margin: 0.5em 0px 1em;">Secara umum, <a class="mw-disambig" href="https://id.wikipedia.org/wiki/Variabel" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Variabel">variabel</a> <i>x</i> dapat berupa bilangan real atau <a href="https://id.wikipedia.org/wiki/Bilangan_kompleks" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan kompleks">bilangan kompleks</a>, ataupun objek matematika yang lain; lihat <a href="https://id.wikipedia.org/wiki/Fungsi_eksponensial#Definisi_formal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">definisi formal di bawah ini</a>.</p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Sifat-sifat">Sifat-sifat</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Fungsi_eksponensial&veaction=edit&section=1" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Sifat-sifat">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Fungsi_eksponensial&action=edit&section=1" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Sifat-sifat">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><p style="margin: 0.5em 0px 1em;">Dengan menggunakan logaritma natural, fungsi eksponensial yang lebih generik dapat didefinisikan. Fungsi</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \!\,a^{x}=e^{x\ln a}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mspace width="negativethinmathspace"></mspace><mspace width="thinmathspace"></mspace><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>=</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mi>ln</mi><mo></mo><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \!\,a^{x}=e^{x\ln a}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f81ce40f1fda846394a70a462f86a480507fbf6f" style="border: 0px; display: inline-block; height: 2.676ex; margin-left: -0.387ex; vertical-align: -0.338ex; width: 11.159ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">yang terdefinisikan untuk <i>a</i> > 0, dan semua bilangan real <i>x</i>, disebut juga <b>fungsi eksponensial dengan basis</b> <i><b>a</b></i>.</p><p style="margin: 0.5em 0px 1em;">Perlu diperhatikan bahwa persamaan tersebut berlaku pula untuk <i>a</i> = <i>e</i>, karena</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \!\,e^{x\ln e}=e^{x\cdot 1}=e^{x}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mspace width="negativethinmathspace"></mspace><mspace width="thinmathspace"></mspace><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mi>ln</mi><mo></mo><mi>�</mi></mrow></msup><mo>=</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mo>⋅</mo><mn>1</mn></mrow></msup><mo>=</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \!\,e^{x\ln e}=e^{x\cdot 1}=e^{x}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1edd058c01b7e4450cdd6a8da7535c13a80b3b1" style="border: 0px; display: inline-block; height: 2.676ex; margin-left: -0.387ex; vertical-align: -0.338ex; width: 18.19ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Fungsi eksponensial dapat "menterjemahkan" antara dua macam operasi, penjumlahan dan pengkalian. Ini dapat dilihat dari <i>rumus-rumus eksponen</i> sebagai berikut:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \!\,a^{0}=1}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mspace width="negativethinmathspace"></mspace><mspace width="thinmathspace"></mspace><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>0</mn></mrow></msup><mo>=</mo><mn>1</mn></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \!\,a^{0}=1}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bfef800064d0e1fdb4a65490ee6f0c575a4b8176" style="border: 0px; display: inline-block; height: 2.676ex; margin-left: -0.387ex; vertical-align: -0.338ex; width: 6.932ex;" /></span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \!\,a^{1}=a}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mspace width="negativethinmathspace"></mspace><mspace width="thinmathspace"></mspace><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msup><mo>=</mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \!\,a^{1}=a}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb5b3c7de4cf518b036352224e055f114e3a5ef8" style="border: 0px; display: inline-block; height: 2.676ex; margin-left: -0.387ex; vertical-align: -0.338ex; width: 6.999ex;" /></span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \!\,a^{x+y}=a^{x}a^{y}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mspace width="negativethinmathspace"></mspace><mspace width="thinmathspace"></mspace><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mo>+</mo><mi>�</mi></mrow></msup><mo>=</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \!\,a^{x+y}=a^{x}a^{y}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c87cdbfa5fc5d2b5f87641f82a146907d06aef8d" style="border: 0px; display: inline-block; height: 2.509ex; margin-left: -0.387ex; vertical-align: -0.338ex; width: 12.665ex;" /></span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \!\,a^{xy}=\left(a^{x}\right)^{y}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mspace width="negativethinmathspace"></mspace><mspace width="thinmathspace"></mspace><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mi>�</mi></mrow></msup><mo>=</mo><msup><mrow><mo>(</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \!\,a^{xy}=\left(a^{x}\right)^{y}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3ace647d06ccb6cb450eae34921cee8f8574dc6" style="border: 0px; display: inline-block; height: 3.009ex; margin-left: -0.387ex; vertical-align: -0.838ex; width: 11.966ex;" /></span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \!\,{1 \over a^{x}}=\left({1 \over a}\right)^{x}=a^{-x}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mspace width="negativethinmathspace"></mspace><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mfrac></mrow><mo>=</mo><msup><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mi>�</mi></mfrac></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>=</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \!\,{1 \over a^{x}}=\left({1 \over a}\right)^{x}=a^{-x}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ddc3b037e77f9c4cc0a60a5c4788b46d2a32e1e" style="border: 0px; display: inline-block; height: 6.176ex; margin-left: -0.387ex; vertical-align: -2.505ex; width: 20.163ex;" /></span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \!\,a^{x}b^{x}=(ab)^{x}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mspace width="negativethinmathspace"></mspace><mspace width="thinmathspace"></mspace><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>=</mo><mo stretchy="false">(</mo><mi>�</mi><mi>�</mi><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \!\,a^{x}b^{x}=(ab)^{x}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffbe7539649d9fe3b8f826f623898c5ad15cdc77" style="border: 0px; display: inline-block; height: 2.843ex; margin-left: -0.387ex; vertical-align: -0.838ex; width: 13.267ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Rumus-rumus di atas berlaku untuk semua bilangan real positif <i>a</i> dan <i>b</i> dan semua bilangan real <i>x</i> dan <i>y</i>. Ekspresi yang mengandung <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Pecahan_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Pecahan (matematika)">pecahan</a> dan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Akar_(matematika)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Akar (matematika) (halaman belum tersedia)">pengakaran</a> pada umumnya dapat disederhanakan dengan menggunakan notasi eksponensial, karena:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {1 \over a}=a^{-1}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mi>�</mi></mfrac></mrow><mo>=</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {1 \over a}=a^{-1}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f53b144185e254fc061ddcacd72b8edd819ba87" style="border: 0px; display: inline-block; height: 5.176ex; vertical-align: -1.838ex; width: 8.727ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">dan, untuk semua <i>a</i> > 0, bilangan real <i>b</i>, dan bilangan bulat <i>n</i> > 1:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {\sqrt[{n}]{a^{b}}}=\left({\sqrt[{n}]{a}}\right)^{b}=a^{b/n}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mroot><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></mroot></mrow><mo>=</mo><msup><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mroot><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></mroot></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>=</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {\sqrt[{n}]{a^{b}}}=\left({\sqrt[{n}]{a}}\right)^{b}=a^{b/n}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4498816147645e1dacd37a88224e3129a7136d0e" style="border: 0px; display: inline-block; height: 3.843ex; vertical-align: -1.005ex; width: 20.576ex;" /></span></dd></dl><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Turunan_dan_persamaan_diferensial">Turunan dan persamaan diferensial</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Fungsi_eksponensial&veaction=edit&section=2" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Turunan dan persamaan diferensial">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Fungsi_eksponensial&action=edit&section=2" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Turunan dan persamaan diferensial">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><p style="margin: 0.5em 0px 1em;">Pentingnya fungsi eksponensial dalam matematika dan ilmu-ilmu lainnya adalah karena sifat <a href="https://id.wikipedia.org/wiki/Turunan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Turunan">turunannya</a>.</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {d \over dx}e^{x}=e^{x}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mi>�</mi><mi>�</mi></mrow></mfrac></mrow><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>=</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {d \over dx}e^{x}=e^{x}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2528d3e349a763e4afd73cddc3ec599ffca15e4" style="border: 0px; display: inline-block; height: 5.509ex; vertical-align: -2.005ex; width: 10.992ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Dengan kata lain, fungsi <i>e</i><sup style="font-size: 11.2px; line-height: 1;"><i>x</i></sup> jika diturunkan, hasilnya adalah fungsi itu sendiri. Sifat "ketidakmempanan untuk diturunkan" ini sangat unik, karena hanya fungsi inilah yang mempunyai sifat seperti ini. Sifat fungsi ini dapat diinterpretasikan sebagai berikut:</p><ul style="list-style-image: url("/w/skins/Vector/resources/skins.vector.styles/images/bullet-icon.svg?d4515"); margin: 0.3em 0px 0px 1.6em; padding: 0px;"><li style="margin-bottom: 0.1em;">Kemiringan (gradien) grafik fungsi ini pada semua titiknya sama dengan nilai fungsi pada titik tersebut.</li><li style="margin-bottom: 0.1em;">Bertambahnya nilai fungsi pada <i>x</i> sama dengan nilai fungsi pada <i>x</i></li><li style="margin-bottom: 0.1em;">Fungsi ini merupakan solusi dari <a href="https://id.wikipedia.org/wiki/Persamaan_diferensial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Persamaan diferensial">persamaan diferensial</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle y'=y}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mo>′</mo></msup><mo>=</mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle y'=y}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6239f12a70a7f715303934acf9dbae208fceb80" style="border: 0px; display: inline-block; height: 2.843ex; vertical-align: -0.671ex; width: 6.099ex;" /></span>.</li></ul><p style="margin: 0.5em 0px 1em;">Dalam ilmu-ilmu terapan, banyak persamaan diferensial yang menghasilkan fungsi eksponensial, antara lain <a href="https://id.wikipedia.org/wiki/Persamaan_Schr%C3%B6dinger" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Persamaan Schrödinger">persamaan Schrödinger</a>, <a href="https://id.wikipedia.org/wiki/Persamaan_Laplace" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Persamaan Laplace">persamaan Laplace</a>, dan persamaan untuk <a class="new" href="https://id.wikipedia.org/w/index.php?title=Gerakan_harmonis_sederhana&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Gerakan harmonis sederhana (halaman belum tersedia)">gerakan harmonis sederhana</a>.</p><p style="margin: 0.5em 0px 1em;">Untuk fungsi eksponensial dengan basis-basis lain (yang bukan <i>e</i>):</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle {d \over dx}a^{x}=(\ln a)a^{x}}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mrow><mi>�</mi><mi>�</mi></mrow></mfrac></mrow><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>=</mo><mo stretchy="false">(</mo><mi>ln</mi><mo></mo><mi>�</mi><mo stretchy="false">)</mo><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup></mstyle></mrow></semantics></math></span><img alt="{\displaystyle {d \over dx}a^{x}=(\ln a)a^{x}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98c4351460316dbd8165d3c60840cbb2e7c59099" style="border: 0px; display: inline-block; height: 5.509ex; vertical-align: -2.005ex; width: 16.65ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">jadi, semua fungsi eksponensial adalah perkalian turunannya sendiri dengan sebuah konstanta.</p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Definisi_formal">Definisi formal</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Fungsi_eksponensial&veaction=edit&section=3" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Definisi formal">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Fungsi_eksponensial&action=edit&section=3" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Definisi formal">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><p style="margin: 0.5em 0px 1em;">Fungsi eksponensial e<sup style="font-size: 11.2px; line-height: 1;"><i>x</i></sup> dapat didefinisikan menurut beberapa definisi yang ekivalen, sebagai <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Deret_tak_terhingga" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Deret tak terhingga">deret tak terhingga</a>. Beberapa definisi tersebut antara lain:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle e^{x}=\sum _{n=0}^{\infty }{x^{n} \over n!}=1+x+{x^{2} \over 2!}+{x^{3} \over 3!}+{x^{4} \over 4!}+\cdots }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>=</mo><munderover><mo>∑</mo><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mo>=</mo><mn>0</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><mrow class="MJX-TeXAtom-ORD"><mfrac><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mrow><mi>�</mi><mo>!</mo></mrow></mfrac></mrow><mo>=</mo><mn>1</mn><mo>+</mo><mi>�</mi><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mrow><mn>2</mn><mo>!</mo></mrow></mfrac></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup><mrow><mn>3</mn><mo>!</mo></mrow></mfrac></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mn>4</mn></mrow></msup><mrow><mn>4</mn><mo>!</mo></mrow></mfrac></mrow><mo>+</mo><mo>⋯</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle e^{x}=\sum _{n=0}^{\infty }{x^{n} \over n!}=1+x+{x^{2} \over 2!}+{x^{3} \over 3!}+{x^{4} \over 4!}+\cdots }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7b3e809a0a747d7caca7a8391cef0c4c66d23fb" style="border: 0px; display: inline-block; height: 6.843ex; vertical-align: -3.005ex; width: 44.657ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">atau sebagai <a class="mw-disambig" href="https://id.wikipedia.org/wiki/Limit" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Limit">limit</a> berikut ini:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle e^{x}=\lim _{n\to \infty }\left(1+{x \over n}\right)^{n}.}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>=</mo><munder><mo form="prefix" movablelimits="true">lim</mo><mrow class="MJX-TeXAtom-ORD"><mi>�</mi><mo stretchy="false">→</mo><mi mathvariant="normal">∞</mi></mrow></munder><msup><mrow><mo>(</mo><mrow><mn>1</mn><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mi>�</mi></mfrac></mrow></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>.</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle e^{x}=\lim _{n\to \infty }\left(1+{x \over n}\right)^{n}.}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/575026a9b5800b841f0f3a53d159d52edec9ba14" style="border: 0px; display: inline-block; height: 4.843ex; vertical-align: -1.838ex; width: 20.889ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Dalam definisi di atas, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle n!}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi><mo>!</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle n!}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bae971720be3cc9b8d82f4cdac89cb89877514a6" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.338ex; width: 2.042ex;" /></span> adalah <a href="https://id.wikipedia.org/wiki/Faktorial" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Faktorial">faktorial</a> dari <i>n</i>, dan <i>x</i> dapat berupa <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Bilangan_real" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan real">bilangan real</a>, <a href="https://id.wikipedia.org/wiki/Bilangan_kompleks" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan kompleks">bilangan kompleks</a>, ataupun konsep-konsep matematika lainnya yang kompleks, seperti matriks bujursangkar (atau <a href="https://id.wikipedia.org/wiki/Matriks_persegi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Matriks persegi">matriks persegi</a>).</p><h2 style="border-bottom: 1px solid rgb(162, 169, 177); color: black; font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Nilai_numerik">Nilai numerik</span><span class="mw-editsection" style="font-family: sans-serif; font-size: small; line-height: 0; margin-left: 1em; margin-right: 0px; unicode-bidi: isolate; user-select: none; vertical-align: baseline;"><span class="mw-editsection-bracket" style="color: #54595d; margin-right: 0.25em;">[</span><a class="mw-editsection-visualeditor" href="https://id.wikipedia.org/w/index.php?title=Fungsi_eksponensial&veaction=edit&section=4" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Sunting bagian: Nilai numerik">sunting</a><span class="mw-editsection-divider" style="color: #54595d;"> | </span><a href="https://id.wikipedia.org/w/index.php?title=Fungsi_eksponensial&action=edit&section=4" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none; text-wrap: nowrap;" title="Edit section's source code: Nilai numerik">sunting sumber</a><span class="mw-editsection-bracket" style="color: #54595d; margin-left: 0.25em;">]</span></span></h2><p style="margin: 0.5em 0px 1em;">Untuk mendapatkan nilai numerik dari fungsi eksponensial, deret tak terhingga di atas dapat ditulis menjadi:</p><dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle e^{x}={1 \over 0!}+x\,\left({1 \over 1!}+x\,\left({1 \over 2!}+x\,\left({1 \over 3!}+\cdots \right)\right)\right)}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>�</mi><mrow class="MJX-TeXAtom-ORD"><mi>�</mi></mrow></msup><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mrow><mn>0</mn><mo>!</mo></mrow></mfrac></mrow><mo>+</mo><mi>�</mi><mspace width="thinmathspace"></mspace><mrow><mo>(</mo><mrow><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mrow><mn>1</mn><mo>!</mo></mrow></mfrac></mrow><mo>+</mo><mi>�</mi><mspace width="thinmathspace"></mspace><mrow><mo>(</mo><mrow><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mrow><mn>2</mn><mo>!</mo></mrow></mfrac></mrow><mo>+</mo><mi>�</mi><mspace width="thinmathspace"></mspace><mrow><mo>(</mo><mrow><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mrow><mn>3</mn><mo>!</mo></mrow></mfrac></mrow><mo>+</mo><mo>⋯</mo></mrow><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle e^{x}={1 \over 0!}+x\,\left({1 \over 1!}+x\,\left({1 \over 2!}+x\,\left({1 \over 3!}+\cdots \right)\right)\right)}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4613ae25244d35a658f4b63e76a22cd5227d1ee0" style="border: 0px; display: inline-block; height: 6.176ex; vertical-align: -2.505ex; width: 46.596ex;" /></span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle =1+{x \over 1}\left(1+{x \over 2}\left(1+{x \over 3}\left(1+\cdots \right)\right)\right)}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>=</mo><mn>1</mn><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mn>1</mn></mfrac></mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mn>2</mn></mfrac></mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>�</mi><mn>3</mn></mfrac></mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>+</mo><mo>⋯</mo></mrow><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle =1+{x \over 1}\left(1+{x \over 2}\left(1+{x \over 3}\left(1+\cdots \right)\right)\right)}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6004040e184ea7fa516f6f3d89c5d4f05faddb0" style="border: 0px; display: inline-block; height: 4.843ex; vertical-align: -1.838ex; width: 36.207ex;" /></span></dd></dl><p style="margin: 0.5em 0px 1em;">Jika x lebih kecil dari 1, maka ekspresi di atas akan menemukan nilai numerik fungsi pada titik yang dicari dengan cepat.</p></div></div></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8185710560472973854.post-90514241395912544682024-01-29T13:35:00.000+07:002024-01-29T13:35:08.962+07:00Aritmetika<p><b style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;">Aritmetika</b><span style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;"> (kadang salah dieja sebagai </span><b style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;">aritmatika</b><span style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;">, berasal dari </span><a href="https://id.wikipedia.org/wiki/Bahasa_Yunani" style="background: none rgb(255, 255, 255); color: #3366cc; font-family: sans-serif; font-size: 14px; overflow-wrap: break-word; text-decoration-line: none;" title="Bahasa Yunani">bahasa Yunani</a><span style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;"> </span><i style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;">αριθμός</i><span style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;"> - </span><i style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;">arithmos</i><span style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;"> = angka) atau dulu disebut </span><b style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;">ilmu hitung</b><span style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;"> merupakan cabang (atau pendahulu) </span><a href="https://id.wikipedia.org/wiki/Matematika" style="background: none rgb(255, 255, 255); color: #3366cc; font-family: sans-serif; font-size: 14px; overflow-wrap: break-word; text-decoration-line: none;" title="Matematika">matematika</a><span style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;"> yang mempelajari </span><i style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;">operasi</i><span style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;"> dasar bilangan. Oleh orang awam, kata "aritmetika" sering dianggap sebagai sinonim dari </span><a href="https://id.wikipedia.org/wiki/Teori_bilangan" style="background: none rgb(255, 255, 255); color: #3366cc; font-family: sans-serif; font-size: 14px; overflow-wrap: break-word; text-decoration-line: none;" title="Teori bilangan">teori bilangan</a><span style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;">. Silakan lihat </span><a class="mw-redirect" href="https://id.wikipedia.org/wiki/Angka" style="background: none rgb(255, 255, 255); color: #3366cc; font-family: sans-serif; font-size: 14px; overflow-wrap: break-word; text-decoration-line: none;" title="Angka">angka</a><span style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;"> untuk mengetahui lebih dalam tentang teori bilangan.</span></p><h2 style="background-color: white; border-bottom: 1px solid rgb(162, 169, 177); font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Sejarah">Sejarah</span></h2><div><span class="mw-headline"><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Prasejarah aritmetika terbatas pada sejumlah kecil artefak, yang dapat menunjukkan konsep penjumlahan dan pengurangan, yang paling terkenal adalah <a href="https://id.wikipedia.org/wiki/Tulang_Ishango" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Tulang Ishango">tulang Ishango</a> dari <a href="https://id.wikipedia.org/wiki/Republik_Demokratik_Kongo" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Republik Demokratik Kongo">Afrika Tengah</a>, berasal dari suatu tempat antara 20.000 dan 18,000 SM, meskipun interpretasinya diperdebatkan.<sup class="reference" id="cite_ref-1" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Aritmetika#cite_note-1" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[1]</a></sup></p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Catatan tertulis paling awal menunjukkan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Matematika_Mesir&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Matematika Mesir (halaman belum tersedia)">Mesir</a> dan <a href="https://id.wikipedia.org/wiki/Matematika_Babilonia" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Matematika Babilonia">Babilonia</a> menggunakan semua operasi <a href="https://id.wikipedia.org/wiki/Aritmetika_dasar" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Aritmetika dasar">aritmetika dasar</a> sejak 2000 SM. Artefak ini tidak selalu mengungkapkan proses spesifik yang digunakan untuk memecahkan masalah, tetapi karakteristik <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Sistem_angka" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Sistem angka">sistem angka</a> tertentu sangat mempengaruhi kompleksitas metode. Sistem hieroglif untuk <a class="new" href="https://id.wikipedia.org/w/index.php?title=Angka_Mesir&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Angka Mesir (halaman belum tersedia)">angka Mesir</a>, seperti kemudian <a href="https://id.wikipedia.org/wiki/Angka_Romawi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Angka Romawi">angka Romawi</a>, diturunkan dari <a class="new" href="https://id.wikipedia.org/w/index.php?title=Tanda_penghitungan&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Tanda penghitungan (halaman belum tersedia)">tanda penghitungan</a> yang digunakan untuk menghitung. Dalam kedua kasus, asal ini menghasilkan nilai yang menggunakan basis <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Desimal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Desimal">desimal</a>, tetapi tidak menyertakan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Notasi_posisi&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Notasi posisi (halaman belum tersedia)">notasi posisi</a>. Perhitungan kompleks dengan angka Romawi membutuhkan bantuan dari <a class="new" href="https://id.wikipedia.org/w/index.php?title=Papan_hitung&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Papan hitung (halaman belum tersedia)">papan hitung</a> (atau <a class="new" href="https://id.wikipedia.org/w/index.php?title=Swipoa_Romawi&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Swipoa Romawi (halaman belum tersedia)">swipoa Romawi</a>) untuk mendapatkan hasil.</p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Sistem bilangan awal yang menyertakan notasi posisi bukanlah desimal, termasuk <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Sexagesimal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Sexagesimal">sexagesimal</a> (basis 60) sistem untuk <a class="new" href="https://id.wikipedia.org/w/index.php?title=Angka_Babilonia&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Angka Babilonia (halaman belum tersedia)">angka Babilonia</a>, dan sistem <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Vigesimal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Vigesimal">vigesimal</a> (basis 20) yang menentukan <a href="https://id.wikipedia.org/wiki/Angka_Maya" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Angka Maya">angka Maya</a>. Karena konsep nilai tempat ini, kemampuan untuk menggunakan kembali angka yang sama untuk nilai yang berbeda berkontribusi pada metode penghitungan yang lebih sederhana dan lebih efisien..</p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Perkembangan historis yang berkelanjutan dari aritmatika modern dimulai dengan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Peradaban_Helenistik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Peradaban Helenistik">peradaban Helenistik</a> dari Yunani kuno, meskipun berasal lebih lama dari contoh Babilonia dan Mesir. Sebelum karya <a href="https://id.wikipedia.org/wiki/Euklides" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Euklides">Euklides</a> sekitar 300 SM, <a href="https://id.wikipedia.org/wiki/Matematika_Yunani" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Matematika Yunani">studi Yunani dalam matematika</a> tumpang tindih dengan keyakinan filosofis dan mistik. Misalnya, <a href="https://id.wikipedia.org/wiki/Nicomachus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Nicomachus">Nicomachus</a> meringkas sudut pandang dari pendekatan <a href="https://id.wikipedia.org/wiki/Pythagoras" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Pythagoras">Pythagoras</a> sebelumnya terhadap angka, dan hubungannya satu sama lain, dalam <i><a class="new" href="https://id.wikipedia.org/w/index.php?title=Pengantar_Aritmetika&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Pengantar Aritmetika (halaman belum tersedia)">Pengantar Aritmetika</a></i>.</p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;"><a href="https://id.wikipedia.org/wiki/Angka_Yunani" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Angka Yunani">Angka Yunani</a> digunakan oleh <a href="https://id.wikipedia.org/wiki/Archimedes" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Archimedes">Archimedes</a>, <a href="https://id.wikipedia.org/wiki/Diophantus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Diophantus">Diophantus</a> dan lainnya dalam <a class="new" href="https://id.wikipedia.org/w/index.php?title=Notasi_posisi&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Notasi posisi (halaman belum tersedia)">notasi posisi</a> yang tidak jauh berbeda dari notasi modern. Orang Yunani kuno tidak memiliki simbol nol sampai periode Helenistik, dan mereka menggunakan tiga set simbol terpisah sebagai <a class="new" href="https://id.wikipedia.org/w/index.php?title=Digit_numerik&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Digit numerik (halaman belum tersedia)">digit</a>: satu set untuk tempat satuan, satu untuk tempat puluhan, dan satu untuk ratusan. Untuk tempat ribuan, mereka akan menggunakan kembali simbol untuk tempat satuan, dan seterusnya. Algoritma penjumlahan mereka identik dengan metode modern, dan algoritma perkaliannya hanya sedikit berbeda. Algoritme pembagian panjangnya sama, dan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Metode_penghitungan_akar_kuadrat&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Metode penghitungan akar kuadrat (halaman belum tersedia)">algoritme akar kuadrat digit demi digit</a>, populer digunakan baru-baru ini pada abad ke-20, dikenal oleh Archimedes (yang mungkin telah menemukannya). Dia lebih memilihnya daripada <a class="new" href="https://id.wikipedia.org/w/index.php?title=Metode_Heron&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Metode Heron (halaman belum tersedia)">Metode Heron</a> dari perkiraan berturut-turut karena, setelah dihitung, sebuah digit tidak berubah, dan akar kuadrat dari kuadrat sempurna, seperti 7485692. Untuk bilangan dengan bagian pecahan, seperti 546,934, mereka menggunakan pangkat negatif 60 bukan pangkat negatif 10 untuk bagian pecahan 0,934.<sup class="reference" id="cite_ref-2" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Aritmetika#cite_note-2" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[2]</a></sup></p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Orang Cina kuno memiliki studi aritmatika lanjutan yang berasal dari Dinasti Shang dan berlanjut hingga <a href="https://id.wikipedia.org/wiki/Dinasti_Tang" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Dinasti Tang">Dinasti Tang</a>, dari angka dasar hingga aljabar lanjutan. The orang Cina kuno menggunakan notasi posisi yang mirip dengan orang Yunani. Karena mereka juga kekurangan simbol untuk <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Nol" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Nol">nol</a>, mereka memiliki satu set simbol untuk tempat satuan, dan set kedua untuk puluhan. Untuk tempat ratusan, mereka kemudian menggunakan kembali simbol untuk tempat satuan, dan seterusnya. Simbol mereka didasarkan pada <a class="new" href="https://id.wikipedia.org/w/index.php?title=Batang_penghitung&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Batang penghitung (halaman belum tersedia)">batang penghitung</a> kuno. Waktu pasti di mana orang Tionghoa mulai menghitung dengan representasi posisi tidak diketahui, meskipun diketahui bahwa adopsi dimulai sebelum 400 SM.<sup class="reference" id="cite_ref-3" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Aritmetika#cite_note-3" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[3]</a></sup> Orang Cina kuno adalah orang pertama yang menemukan, memahami, dan menerapkan angka negatif secara bermakna. Ini dijelaskan di <i><a class="new" href="https://id.wikipedia.org/w/index.php?title=Sembilan_Bab_tentang_Seni_Matematika&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Sembilan Bab tentang Seni Matematika (halaman belum tersedia)">Sembilan Bab tentang Seni Matematika</a></i> (<i>Jiuzhang Suanshu</i>), yang ditulis oleh <a href="https://id.wikipedia.org/wiki/Liu_Hui" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Liu Hui">Liu Hui</a> berasal dari abad ke-2 SM.</p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Perkembangan bertahap dari <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Sistem_angka_Hindu-Arab" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Sistem angka Hindu-Arab">sistem angka Hindu-Arab</a> secara independen menciptakan konsep nilai tempat dan notasi posisi, yang menggabungkan metode sederhana untuk komputasi dengan basis desimal, dan penggunaan digit yang mewakili <a href="https://id.wikipedia.org/wiki/0_(angka)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="0 (angka)">0</a>. Hal ini memungkinkan sistem untuk secara konsisten mewakili bilangan bulat besar dan kecil, sebuah pendekatan yang pada akhirnya menggantikan semua sistem lainnya. Di awal <span class="nowrap" style="text-wrap: nowrap;">Abad ke-6 Masehi,</span> matematikawan asal India <a href="https://id.wikipedia.org/wiki/Aryabhata" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Aryabhata">Aryabhata</a> memasukkan versi yang ada dari sistem ini dalam karyanya, dan bereksperimen dengan notasi yang berbeda. Pada abad ke-7, <a href="https://id.wikipedia.org/wiki/Brahmagupta" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Brahmagupta">Brahmagupta</a> menetapkan penggunaan 0 sebagai bilangan terpisah, dan menentukan hasil perkalian, pembagian, penambahan dan pengurangan nol dan semua bilangan lainnya — kecuali untuk hasil <a class="new" href="https://id.wikipedia.org/w/index.php?title=Pembagian_dengan_nol&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Pembagian dengan nol (halaman belum tersedia)">pembagian dengan nol</a>. Sesamannya, uskup <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Kristen_Siria" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kristen Siria">Siria</a> <a href="https://id.wikipedia.org/wiki/Severus_Sebokht" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Severus Sebokht">Severus Sebokht</a> (650 M) berkata, "Orang India memiliki metode perhitungan yang tidak dapat dipuji oleh satu kata pun. Sistem matematika rasional mereka, atau metode perhitungan mereka. Maksud saya sistemnya menggunakan sembilan simbol."<sup class="reference" id="cite_ref-4" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Aritmetika#cite_note-4" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[4]</a></sup> Orang Arab juga mempelajari metode baru ini dan menyebutnya <i>hesab</i>.</p><figure style="background-color: #f8f9fa; border-bottom-color: initial; border-bottom-style: initial; border-collapse: collapse; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: rgb(200, 204, 209); border-top-style: solid; border-width: 1px 1px 0px; clear: right; color: #202122; display: table; float: right; font-family: sans-serif; font-size: 14px; line-height: 0; margin: 0.5em 0px 1.3em 1.4em; min-width: 100px; text-align: center;" typeof="mw:File/Thumb"><a class="mw-file-description" href="https://id.wikipedia.org/wiki/Berkas:Leibniz_Stepped_Reckoner.png" style="background: none; border: 0px; color: #3366cc; display: block; overflow-wrap: break-word; position: relative; text-decoration-line: none;"><img class="mw-file-element" data-file-height="803" data-file-width="1235" decoding="async" height="130" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Leibniz_Stepped_Reckoner.png/200px-Leibniz_Stepped_Reckoner.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Leibniz_Stepped_Reckoner.png/300px-Leibniz_Stepped_Reckoner.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Leibniz_Stepped_Reckoner.png/400px-Leibniz_Stepped_Reckoner.png 2x" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1px solid rgb(200, 204, 209); margin: 3px; vertical-align: middle;" width="200" /></a><figcaption style="border-bottom-color: rgb(200, 204, 209); border-bottom-style: solid; border-image: initial; border-left-color: rgb(200, 204, 209); border-left-style: solid; border-right-color: rgb(200, 204, 209); border-right-style: solid; border-top-color: initial; border-top-style: initial; border-width: 0px 1px 1px; caption-side: bottom; display: table-caption; font-size: 12.376px; line-height: 1.4em; padding: 0px 6px 6px; text-align: left; word-break: break-word;">Leibniz's <a class="new" href="https://id.wikipedia.org/w/index.php?title=Stepped_Reckoner&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Stepped Reckoner (halaman belum tersedia)">Stepped Reckoner</a> adalah kalkulator pertama yang bisa melakukan keempat operasi aritmatika.</figcaption></figure><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Meskipun <a href="https://id.wikipedia.org/wiki/Codex_Vigilanus" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Codex Vigilanus">Codex Vigilanus</a> menggambarkan bentuk awal angka Arab (menghilangkan 0) pada 976 M, Leonardo dari Pisa (<a class="mw-redirect" href="https://id.wikipedia.org/wiki/Fibonacci" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fibonacci">Fibonacci</a>) bertanggung jawab terutama untuk menyebarkan penggunaannya ke seluruh Eropa setelah penerbitan bukunya <i><a class="new" href="https://id.wikipedia.org/w/index.php?title=Liber_Abaci&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Liber Abaci (halaman belum tersedia)">Liber Abaci</a></i> pada 1202. Dia menulis, "Metode orang India (Latin <i>Modus Indoram</i>) melampaui metode komputasi apa pun yang diketahui. Itu metode yang luar biasa. Mereka melakukan komputasi menggunakan sembilan angka dan simbol <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Nol" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Nol">nol</a>".<sup class="reference" id="cite_ref-5" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Aritmetika#cite_note-5" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[5]</a></sup></p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Pada Abad Pertengahan, aritmatika adalah salah satu dari tujuh <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Seni_liberal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Seni liberal">seni liberal</a> yang diajarkan di universitas.</p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Berkembangnya <a href="https://id.wikipedia.org/wiki/Aljabar" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Aljabar">aljabar</a> di dunia <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Abad_pertengahan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Abad pertengahan">abad pertengahan</a> <a href="https://id.wikipedia.org/wiki/Islam" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Islam">Islam</a>, dan juga di <a href="https://id.wikipedia.org/wiki/Renaisans" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Renaisans">Renaisans</a> <a href="https://id.wikipedia.org/wiki/Eropa" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Eropa">Eropa</a>, adalah hasil dari penyederhanaan <a href="https://id.wikipedia.org/wiki/Komputasi" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Komputasi">komputasi</a> melalui <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Desimal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Desimal">desimal</a> bukan.</p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Berbagai jenis alat telah ditemukan dan digunakan secara luas untuk membantu dalam perhitungan numerik. Sebelum Renaisans, mereka adalah berbagai jenis <a class="new" href="https://id.wikipedia.org/w/index.php?title=Abaci&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Abaci (halaman belum tersedia)">abaci</a>. Contoh yang lebih baru termasuk <a class="new" href="https://id.wikipedia.org/w/index.php?title=Aturan_geser&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Aturan geser (halaman belum tersedia)">aturan geser</a> s, <a class="new" href="https://id.wikipedia.org/w/index.php?title=Nomogram&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Nomogram (halaman belum tersedia)">nomogram</a> dan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Kalkulator_mekanis&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Kalkulator mekanis (halaman belum tersedia)">kalkulator mekanis</a>, seperti <a href="https://id.wikipedia.org/wiki/Kalkulator_Pascal" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kalkulator Pascal">kalkulator Pascal</a>. Saat ini, mereka telah digantikan oleh <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Kalkulator" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Kalkulator">kalkulator</a> dan <a href="https://id.wikipedia.org/wiki/Komputer" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Komputer">komputer</a> elektronik.</p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;"><br /></p><h2 style="background-color: white; border-bottom: 1px solid rgb(162, 169, 177); font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Operasi_aritmetika">Operasi aritmetika</span></h2><div class="hatnote navigation-not-searchable" role="note" style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; font-style: italic; margin-bottom: 0.5em; padding-left: 1.6em;">Lihat pula: <a href="https://id.wikipedia.org/wiki/Operasi_aljabar" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Operasi aljabar">Operasi aljabar</a></div><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Operasi aritmatika dasar adalah penjumlahan, pengurangan, perkalian dan pembagian, meskipun mata pelajaran ini juga mencakup operasi yang lebih maju, seperti manipulasi <a href="https://id.wikipedia.org/wiki/Persentase" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Persentase">persentase</a>,<sup class="reference" id="cite_ref-:2_6-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Aritmetika#cite_note-:2-6" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[6]</a></sup> <a href="https://id.wikipedia.org/wiki/Akar_kuadrat" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Akar kuadrat">akar kuadrat</a> s, <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Eksponen" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Eksponen">eksponen</a>, <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Fungsi_logaritmik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi logaritmik">fungsi logaritmik</a>, dan bahkan <a href="https://id.wikipedia.org/wiki/Fungsi_trigonometri" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi trigonometri">fungsi trigonometri</a>, dalam nada yang sama seperti logaritma (<a class="new" href="https://id.wikipedia.org/w/index.php?title=Prosthaphaeresis&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Prosthaphaeresis (halaman belum tersedia)">prosthaphaeresis</a>). Ekspresi aritmatika harus dievaluasi sesuai dengan urutan operasi yang dimaksudkan. Ada beberapa metode untuk menentukan ini, baik yang paling umum, bersama dengan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Notasi_infix&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Notasi infix (halaman belum tersedia)">notasi infix</a>, secara eksplisit menggunakan tanda kurung dan bergantung pada <a class="new" href="https://id.wikipedia.org/w/index.php?title=Urutan_operasi_aturan_prioritas&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Urutan operasi aturan prioritas (halaman belum tersedia)">Urutan operasi aturan prioritas</a>, atau menggunakan notasi <a class="new" href="https://id.wikipedia.org/w/index.php?title=Notasi_Polandia&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Notasi Polandia (halaman belum tersedia)">awalan</a> atau <a class="new" href="https://id.wikipedia.org/w/index.php?title=Notasi_Polandia_terbalik&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Notasi Polandia terbalik (halaman belum tersedia)">postfix</a>, yang secara unik memperbaiki urutan eksekusi sendiri. Kumpulan objek apa pun di mana keempat operasi aritmatika (kecuali <a class="new" href="https://id.wikipedia.org/w/index.php?title=Pembagian_dengan_nol&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Pembagian dengan nol (halaman belum tersedia)">pembagian dengan nol</a>) dapat dilakukan, dan di mana keempat operasi ini mematuhi hukum biasa (termasuk distribusi), disebut <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Bidang_matematika" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bidang matematika">bidang</a>.<sup class="reference" id="cite_ref-Oxford_7-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Aritmetika#cite_note-Oxford-7" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[7]</a></sup></p><h3 style="background-color: white; font-family: sans-serif; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Penambahan">Penambahan</span></h3><div class="hatnote navigation-not-searchable" role="note" style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; font-style: italic; margin-bottom: 0.5em; padding-left: 1.6em;">Artikel utama: <a href="https://id.wikipedia.org/wiki/Penambahan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Penambahan">Penambahan</a></div><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Penjumlahan, dilambangkan dengan simbol <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle +}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>+</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle +}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe6ef363cd19902d1a7a71fb1c8b21e8ede52406" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.505ex; width: 1.808ex;" /></span>, adalah operasi aritmatika yang paling dasar. Dalam bentuk sederhananya, penjumlahan menggabungkan dua angka, <i>penjumlahan </i>atau <i><a class="new" href="https://id.wikipedia.org/w/index.php?title=Suku_(matematika)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Suku (matematika) (halaman belum tersedia)">suku</a></i>, menjadi satu angka, <i>jumlah</i> dari angka-angka tersebut (seperti <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">2 + 2 = 4</span> atau <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">3 + 5 = 8</span>).</p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Menambahkan banyak angka secara tak terbatas dapat dipandang sebagai penjumlahan sederhana yang berulang; prosedur ini dikenal sebagai <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Penjumlahan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Penjumlahan">penjumlahan</a>, istilah yang juga digunakan untuk menunjukkan definisi untuk "menambahkan bilangan tak terhingga" dalam <a href="https://id.wikipedia.org/wiki/Deret_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Deret (matematika)">deret tak hingga</a>. Penambahan berulang dari angka <a href="https://id.wikipedia.org/wiki/1_(angka)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="1 (angka)">1</a> adalah bentuk paling dasar dari <a class="new" href="https://id.wikipedia.org/w/index.php?title=Menghitung&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Menghitung (halaman belum tersedia)">menghitung</a>; hasil penambahan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">1</span> biasanya disebut <a class="new" href="https://id.wikipedia.org/w/index.php?title=Fungsi_penerus&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Fungsi penerus (halaman belum tersedia)">penerus</a> dari <a href="https://id.wikipedia.org/wiki/Bilangan_asli" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan asli">bilangan asli</a>.</p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Penjumlahan adalah <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Komutatif" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Komutatif">komutatif</a> dan <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Asosiatif" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Asosiatif">asosiatif</a>, jadi urutan penambahan banyak suku tidak menjadi masalah. <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Elemen_identitas" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Elemen identitas">Elemen identitas</a> untuk <a href="https://id.wikipedia.org/wiki/Operasi_biner" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Operasi biner">operasi biner</a> adalah angka yang, jika digabungkan dengan angka apa pun, menghasilkan angka yang sama dengan hasil. Menurut aturan penambahan, penambahan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">0</span> ke nomor manapun menghasilkan nomor yang sama, jadi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">0</span> adalah <a class="new" href="https://id.wikipedia.org/w/index.php?title=Identitas_aditif&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Identitas aditif (halaman belum tersedia)">identitas aditif</a>.<sup class="reference" id="cite_ref-:0_8-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Aritmetika#cite_note-:0-8" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[8]</a></sup> The <i><a href="https://id.wikipedia.org/wiki/Elemen_invers" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Elemen invers">invers</a> dari sebuah bilangan</i> sehubungan dengan sebuah <a href="https://id.wikipedia.org/wiki/Operasi_biner" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Operasi biner">operasi biner</a> adalah bilangan yang, jika digabungkan dengan bilangan apa pun, menghasilkan identitas sehubungan dengan operasi ini. Jadi, kebalikan dari bilangan sehubungan dengan penjumlahan (<a class="new" href="https://id.wikipedia.org/w/index.php?title=Pembalikan_aditif&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Pembalikan aditif (halaman belum tersedia)">pembalikan aditif</a>, atau bilangan kebalikannya) adalah bilangan yang menghasilkan identitas penjumlahan, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">0</span>, ketika ditambahkan ke nomor asli; terlihat jelas bahwa untuk semua bilangan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" style="border: 0px; display: inline-block; height: 1.676ex; margin: 0px; vertical-align: -0.338ex; width: 1.33ex;" /></span>, ini adalah negatif dari <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" style="border: 0px; display: inline-block; height: 1.676ex; margin: 0px; vertical-align: -0.338ex; width: 1.33ex;" /></span> (dilambangkan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle -x}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>−</mo><mi>�</mi></mstyle></mrow></semantics></math></span><img alt="{\displaystyle -x}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae55e66aeffc525917eed885b4b753ba5a7f8b3e" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.505ex; width: 3.138ex;" /></span>).<sup class="reference" id="cite_ref-:0_8-1" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Aritmetika#cite_note-:0-8" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[8]</a></sup> Misalnya, aditif invers <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">7</span> adalah <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">−7</span>, maka <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">7 + (−7) = 0</span>.</p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Penambahan juga dapat diartikan secara geometris, seperti pada contoh berikut:</p><dl style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;">Jika kita memiliki dua batang dengan panjang <i>2 </i>dan <i>5 </i>, maka, jika kita menempatkan tongkat satu per satu, panjang tongkat menjadi <i>7 </i>, karena <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">2 + 5 = 7</span>.</dd></dl><h3 style="background-color: white; font-family: sans-serif; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Pengurangan">Pengurangan</span></h3><div class="hatnote navigation-not-searchable" role="note" style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; font-style: italic; margin-bottom: 0.5em; padding-left: 1.6em;">Artikel utama: <a href="https://id.wikipedia.org/wiki/Pengurangan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Pengurangan">Pengurangan</a></div><div class="hatnote navigation-not-searchable" role="note" style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; font-style: italic; margin-bottom: 0.5em; margin-top: -0.5em; padding-left: 1.6em;">Lihat pula: <a class="new" href="https://id.wikipedia.org/w/index.php?title=Metode_pelengkap&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Metode pelengkap (halaman belum tersedia)">Metode pelengkap</a></div><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Pengurangan, dilambangkan dengan simbol <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle -}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>−</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle -}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04bd52ce670743d3b61bec928a7ec9f47309eb36" style="border: 0px; display: inline-block; height: 2.176ex; margin: 0px; vertical-align: -0.505ex; width: 1.808ex;" /></span>, adalah operasi kebalikan dari penjumlahan. Pengurangan menemukan <i>perbedaan </i>antara dua angka, <i>minuend </i>dikurangi <i>subtrahend </i>: <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>D</i> = <i>M</i> − <i>S</i>.</span> Menggunakan penambahan yang telah ditetapkan sebelumnya, ini berarti bahwa perbedaannya adalah angka yang, ketika ditambahkan ke subtrahend, menghasilkan minuend: <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>D</i> + <i>S</i> = <i>M</i>.</span><sup class="reference" id="cite_ref-:1_9-0" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Aritmetika#cite_note-:1-9" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[9]</a></sup></p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Untuk argumen positif <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">M</span> dan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">S</span> berlaku:</p><dl style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;">Jika minuend lebih besar dari subtrahend, perbedaan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">D</span> positif.</dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;">Jika minuend lebih kecil dari subtrahend, perbedaan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">D</span> adalah negatif.</dd></dl><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Bagaimanapun, jika minuend dan subtrahend sama, selisihnya <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>D</i> = 0.</span></p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Pengurangan bukan <a href="https://id.wikipedia.org/wiki/Sifat_komutatif" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Sifat komutatif">komutatif</a> atau <a class="new" href="https://id.wikipedia.org/w/index.php?title=Sifta_asosiatif&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Sifta asosiatif (halaman belum tersedia)">asosiatif</a>. Oleh karena itu, konstruksi operasi inversi dalam aljabar modern sering kali diabaikan demi pengenalan konsep elemen invers (seperti yang digambarkan di bawah). <a href="https://id.wikipedia.org/wiki/Aritmetika#Penambahan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">§ Penambahan</a>), di mana pengurangan dianggap menambahkan invers penjumlahan dari pengurang ke minuend, yaitu, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>a</i> − <i>b</i> = <i>a</i> + (−<i>b</i>)</span>. Harga langsung untuk membuang operasi pengurangan biner adalah pengenalan dari (trivial) <a class="new" href="https://id.wikipedia.org/w/index.php?title=Operasi_unary&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Operasi unary (halaman belum tersedia)">operasi unary</a>, memberikan invers penjumlahan untuk bilangan tertentu, dan kehilangan akses langsung ke gagasan <a class="mw-disambig" href="https://id.wikipedia.org/wiki/Diferensial_(matematika)" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Diferensial (matematika)">perbedaan</a>, yang berpotensi menyesatkan ketika argumen negatif terlibat.</p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Untuk representasi bilangan apa pun, ada metode untuk menghitung hasil, beberapa di antaranya sangat menguntungkan dalam prosedur pemanfaatan, yang ada untuk satu operasi, dengan perubahan kecil juga. Misalnya, komputer digital dapat menggunakan kembali sirkuit tambahan yang ada dan menyimpan sirkuit tambahan untuk menerapkan pengurangan, dengan menggunakan metode <a class="new" href="https://id.wikipedia.org/w/index.php?title=Komplemen_dua&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Komplemen dua (halaman belum tersedia)">komplemen dua</a> untuk mewakili invers aditif, yang sangat mudah diterapkan di perangkat keras (<a class="new" href="https://id.wikipedia.org/w/index.php?title=Inverter_(gerbang_logika)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Inverter (gerbang logika) (halaman belum tersedia)">negasi</a>). Pengorbanannya adalah membagi separuh rentang angka untuk panjang kata yang tetap.</p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Metode yang sebelumnya tersebar luas untuk mencapai jumlah perubahan yang benar, mengetahui jumlah yang jatuh tempo dan jumlah yang diberikan, adalah <i>metode penghitungan </i>, yang tidak secara eksplisit menghasilkan nilai perbedaan. Misalkan sejumlah <i>P </i>diberikan untuk membayar jumlah yang dibutuhkan <i>Q </i>, dengan <i>P </i>lebih besar dari <i>Q </i>. Daripada melakukan pengurangan secara eksplisit <i>P</i> − <i>Q</i> = <i>C</i> dan menghitung jumlah <i>C </i>dalam kembalian, uang dihitung dimulai dengan penerus <i>Q </i>, dan dilanjutkan dengan langkah mata uang, sampai <i>P </i>tercapai. Meskipun jumlah yang dihitung harus sama dengan hasil pengurangan <i>P </i>- <i>Q </i>, pengurangan tidak pernah benar-benar dilakukan dan nilai <i>P </i>- <i>Q </i>tidak diberikan oleh ini metode.</p><h3 style="background-color: white; font-family: sans-serif; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Perkalian">Perkalian</span></h3><div class="hatnote navigation-not-searchable" role="note" style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; font-style: italic; margin-bottom: 0.5em; padding-left: 1.6em;">Artikel utama: <a href="https://id.wikipedia.org/wiki/Perkalian" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Perkalian">Perkalian</a></div><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Perkalian, dilambangkan dengan simbol <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \times }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>×</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \times }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ffafff1ad26cbe49045f19a67ce532116a32703" style="border: 0px; display: inline-block; height: 1.509ex; margin: 0px 0px -0.19ex; vertical-align: 0.019ex; width: 1.808ex;" /></span> atau <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \cdot }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>⋅</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \cdot }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba2c023bad1bd39ed49080f729cbf26bc448c9ba" style="border: 0px; display: inline-block; height: 1.176ex; margin: 0px 0px -0.61ex; vertical-align: 0.439ex; width: 0.647ex;" /></span>,<sup class="reference" id="cite_ref-:0_8-2" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Aritmetika#cite_note-:0-8" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[8]</a></sup> adalah operasi dasar kedua dari aritmatika. Perkalian juga menggabungkan dua angka menjadi satu angka, <i>hasil kali </i>. Dua angka asli disebut <i>pengganda </i>dan <i>perkalian </i>, kebanyakan keduanya disebut <i>faktor </i>.</p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Perkalian dapat dilihat sebagai operasi penskalaan. Jika angka-angka tersebut dibayangkan berada dalam satu garis, perkalian dengan angka yang lebih besar dari 1, katakan <i>x </i>, sama dengan merentangkan semuanya dari 0 secara seragam, sedemikian rupa sehingga angka 1 itu sendiri direntangkan ke tempat <i>x </i>sebelumnya. Demikian pula, mengalikan dengan angka kurang dari 1 dapat dibayangkan sebagai meremas ke arah 0, sedemikian rupa sehingga 1.</p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Pandangan lain tentang perkalian bilangan bulat (dapat diperpanjang ke rasio tetapi tidak dapat diakses untuk bilangan real) adalah dengan menganggapnya sebagai penjumlahan berulang. Sebagai contoh. <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">3 × 4</span> sesuai dengan penambahan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">3</span> kali <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">4</span>, atau <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">4</span> kali <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">3</span>, memberikan hasil yang sama. Ada beberapa pendapat berbeda tentang keuntungan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Perkalian_dan_penjumlahan_berulang&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Perkalian dan penjumlahan berulang (halaman belum tersedia)">paradigmata</a> ini dalam pendidikan matematika.</p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Perkalian bersifat komutatif dan asosiatif; selanjutnya, <a class="new" href="https://id.wikipedia.org/w/index.php?title=Distributivitas&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Distributivitas (halaman belum tersedia)">distributif</a> melebihi penjumlahan dan pengurangan. <a class="new" href="https://id.wikipedia.org/w/index.php?title=Identitas_perkalian&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Identitas perkalian (halaman belum tersedia)">Identitas perkalian</a> adalah 1,<sup class="reference" id="cite_ref-:0_8-3" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Aritmetika#cite_note-:0-8" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[8]</a></sup> karena mengalikan angka apa pun dengan 1 menghasilkan angka yang sama. <a class="new" href="https://id.wikipedia.org/w/index.php?title=Pembalikan_perkalian&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Pembalikan perkalian (halaman belum tersedia)">Pembalikan perkalian</a> untuk bilangan apa pun kecuali <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">0</span> adalah <a class="new" href="https://id.wikipedia.org/w/index.php?title=Kebalikan_(matematika)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Kebalikan (matematika) (halaman belum tersedia)">kebalikan</a> dari bilangan ini, karena mengalikan kebalikan dari bilangan apa pun dengan bilangan itu sendiri menghasilkan identitas perkalian <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">1</span>. <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">0</span> Adalah satu-satunya bilangan tanpa pembalikan perkalian, dan hasil dari mengalikan bilangan apa pun dan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">0</span> adalah lagi <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">0.</span> One says that <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">0</span> is tidak terkandung dalam perkalian <a class="new" href="https://id.wikipedia.org/w/index.php?title=Kelompok_(matematika)&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Kelompok (matematika) (halaman belum tersedia)">kelompok</a> dari bilangan tersebut.</p><h3 style="background-color: white; font-family: sans-serif; font-size: 1.2em; line-height: 1.6; margin: 0.3em 0px 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0.5em;"><span class="mw-headline" id="Pembagian">Pembagian</span></h3><div class="hatnote navigation-not-searchable" role="note" style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; font-style: italic; margin-bottom: 0.5em; padding-left: 1.6em;">Artikel utama: <a href="https://id.wikipedia.org/wiki/Pembagian" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Pembagian">Pembagian</a></div><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Divisi, dilambangkan dengan simbol <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle \div }" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>÷</mo></mstyle></mrow></semantics></math></span><img alt="{\displaystyle \div }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/837b35ee5d25b5ce7b07f292c27cc90533dd9fd4" style="border: 0px; display: inline-block; height: 1.843ex; margin: 0px; vertical-align: -0.338ex; width: 1.808ex;" /></span> or <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="clip: rect(1px, 1px, 1px, 1px); display: none; font-size: 16.52px; height: 1px; opacity: 0; overflow: hidden; position: absolute; width: 1px;"><math alttext="{\displaystyle /}" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow></mstyle></mrow></semantics></math></span><img alt="{\displaystyle /}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da0c4de1fba637d9799f6c64a6c77bf016d0ce1e" style="border: 0px; display: inline-block; height: 2.843ex; margin: 0px; vertical-align: -0.838ex; width: 1.162ex;" /></span>,<sup class="reference" id="cite_ref-:0_8-4" style="font-size: 11.2px; line-height: 1; text-wrap: nowrap; unicode-bidi: isolate;"><a href="https://id.wikipedia.org/wiki/Aritmetika#cite_note-:0-8" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">[8]</a></sup> pada dasarnya adalah operasi kebalikan dari perkalian. Pembagian menemukan <i>hasil bagi </i>dari dua angka, <i>pembilang </i>dibagi dengan <i>pembagi </i>. Setiap dividen <a class="new" href="https://id.wikipedia.org/w/index.php?title=Pembagian_dengan_nol&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Pembagian dengan nol (halaman belum tersedia)">dibagi dengan nol</a> tidak ditentukan. Untuk bilangan positif berbeda, jika pembagi lebih besar dari pembagi, hasil bagi lebih besar dari 1, jika tidak, kurang dari 1 (aturan serupa berlaku untuk angka negatif). Hasil bagi dikalikan dengan pembagi selalu menghasilkan dividen.</p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Pembagian tidak bersifat komutatif atau asosiatif. Demikian seperti yang dijelaskan di <a href="https://id.wikipedia.org/wiki/Aritmetika#Pengurangan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">§ Pengurangan</a>, konstruksi pembagian dalam aljabar modern dibuang demi membangun elemen invers sehubungan dengan perkalian, seperti yang diperkenalkan di <a href="https://id.wikipedia.org/wiki/Aritmetika#Perkalian" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;">§ Perkalian</a>. Oleh karena itu, pembagian adalah perkalian dividen dengan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Pembalikan_perkalian&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Pembalikan perkalian (halaman belum tersedia)">kebalikan</a> dari pembagi sebagai faktor, yaitu, <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>a</i> ÷ <i>b</i> = <i>a</i> × <span class="sfrac nowrap" style="display: inline-block; font-size: 14.042px; text-align: center; vertical-align: -0.5em;"><span style="display: block; line-height: 1em; margin: 0px 0.1em;">1</span><span style="border-top: 1px solid; display: block; line-height: 1em; margin: 0px 0.1em;"><i>b</i></span></span>.</span></p><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Di dalam bilangan asli, ada juga gagasan berbeda namun terkait yang disebut <a class="new" href="https://id.wikipedia.org/w/index.php?title=Pembagian_euklidean&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Pembagian euklidean (halaman belum tersedia)">Pembagian euklidean</a>, yang mengeluarkan dua bilangan setelah "membagi" <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">N</span> (pembilang) alami dengan <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">C</span>): pertama natural <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">Q</span> (hasil bagi), dan kedua natural <span class="texhtml mvar" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-style: italic; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">R</span> (sisa) sehingga <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;"><i>N</i> = <i>D</i>×<i>Q</i> + <i>R</i></span> dan <span class="texhtml" style="font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; text-wrap: nowrap;">0 ≤ <i>R</i> < <i>Q</i>.</span></p><h2 style="background-color: white; border-bottom: 1px solid rgb(162, 169, 177); font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Teorema_dasar_aritmetika">Teorema dasar aritmetika</span></h2><div class="hatnote navigation-not-searchable" role="note" style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; font-style: italic; margin-bottom: 0.5em; padding-left: 1.6em;">Artikel utama: <a href="https://id.wikipedia.org/wiki/Teorema_dasar_aritmetika" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teorema dasar aritmetika">Teorema dasar aritmetika</a></div><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;"><b>Teorema dasar aritmatika</b>menyatakan bahwa bilangan bulat apa pun yang lebih besar dari 1 memiliki <a href="https://id.wikipedia.org/wiki/Faktorisasi_prima" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Faktorisasi prima">faktorisasi prima</a> unik (representasi bilangan sebagai hasil kali faktor prima), tidak termasuk urutan faktor. Misalnya, 252 hanya memiliki satu faktorisasi prima:</p><dl style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;">252 = 2<sup style="font-size: 11.2px; line-height: 1;">2</sup> × 3<sup style="font-size: 11.2px; line-height: 1;">2</sup> × 7<sup style="font-size: 11.2px; line-height: 1;">1</sup></dd></dl><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;"><a href="https://id.wikipedia.org/wiki/Elemen_Euklides" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Elemen Euklides">Elemen Euklides</a> pertama kali memperkenalkan teorema ini, dan memberikan bukti parsial (yang disebut <a class="new" href="https://id.wikipedia.org/w/index.php?title=Lemma_Euklides&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Lemma Euklides (halaman belum tersedia)">lemma Euklides</a>). Teorema dasar aritmatika pertama kali dibuktikan oleh <a href="https://id.wikipedia.org/wiki/Carl_Friedrich_Gauss" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Carl Friedrich Gauss">Carl Friedrich Gauss</a>.</p><h2 style="background-color: white; border-bottom: 1px solid rgb(162, 169, 177); font-family: "Linux Libertine", Georgia, Times, "Source Serif Pro", serif; font-weight: normal; line-height: 1.375; margin: 1em 0px 0.25em; overflow: hidden; padding: 0px;"><span class="mw-headline" id="Teori_bilangan">Teori bilangan</span></h2><div class="hatnote navigation-not-searchable" role="note" style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; font-style: italic; margin-bottom: 0.5em; padding-left: 1.6em;">Artikel utama: <a href="https://id.wikipedia.org/wiki/Teori_bilangan" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teori bilangan">Teori bilangan</a></div><p style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px; margin: 0.5em 0px 1em;">Sampai abad ke-19, <i>teori bilangan </i>adalah sinonim dari "aritmatika". Masalah yang ditangani secara langsung terkait dengan operasi dasar dan terkait <a href="https://id.wikipedia.org/wiki/Bilangan_prima" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Bilangan prima">primality</a>, <a class="new" href="https://id.wikipedia.org/w/index.php?title=Terbagi&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Terbagi (halaman belum tersedia)">terbagi</a>, dan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Persamaan_Diophantine&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Persamaan Diophantine (halaman belum tersedia)">solusi persamaan dalam bilangan bulat</a>, seperti <a class="mw-redirect" href="https://id.wikipedia.org/wiki/Teorema_terakhir_Fermat" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teorema terakhir Fermat">teorema terakhir Fermat</a>. Tampaknya sebagian besar masalah ini, meskipun sangat mendasar untuk dinyatakan, sangat sulit dan mungkin tidak dapat diselesaikan tanpa matematika yang sangat mendalam yang melibatkan konsep dan metode dari banyak cabang lain. Hal ini menyebabkan cabang baru dari teori bilangan seperti <a href="https://id.wikipedia.org/wiki/Teori_bilangan_analitik" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teori bilangan analitik">teori bilangan analitik</a>, <a href="https://id.wikipedia.org/wiki/Teori_bilangan_aljabar" style="background: none; color: #3366cc; overflow-wrap: break-word; text-decoration-line: none;" title="Teori bilangan aljabar">teori bilangan aljabar</a>, <a class="new" href="https://id.wikipedia.org/w/index.php?title=Geometri_diofantin&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Geometri diofantin (halaman belum tersedia)">geometri diofantin</a> dan <a class="new" href="https://id.wikipedia.org/w/index.php?title=Geometri_aljabar_aritmatika&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Geometri aljabar aritmatika (halaman belum tersedia)">geometri aljabar aritmatika</a>. <a class="new" href="https://id.wikipedia.org/w/index.php?title=Bukti_Wiles_tentang_Teorema_Terakhir_Fermat&action=edit&redlink=1" style="background: none; color: #d73333; overflow-wrap: break-word; text-decoration-line: none;" title="Bukti Wiles tentang Teorema Terakhir Fermat (halaman belum tersedia)">Bukti Wiles tentang Teorema Terakhir Fermat</a> adalah contoh khas perlunya metode canggih, yang jauh melampaui metode aritmatika klasik, untuk memecahkan masalah yang dapat dinyatakan dalam aritmatika dasar.</p></span></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8185710560472973854.post-89069071535649358732023-11-20T05:26:00.015+07:002023-11-23T12:48:07.347+07:00Kisi-kisi Soal PAS Fisika Kelas 12<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEitnh4ug_0B-lREOCs4iRqETlHUUYhCN1H2e_QO_iYiWbNvf0NkXpzRs590hLJTq47LZfNqb-CFXFPMpxo0CXhzJnTuPN1LzVf3bqxq_aYXb1hJPnUGqP4AGVdi1mP_1QdP6dBb3_ONoSOtQe4gM8sLnTma4tcbM9MlUIjZz-0YYSClphgm_xHegDOWZ1A" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="417" data-original-width="839" height="318" src="https://blogger.googleusercontent.com/img/a/AVvXsEitnh4ug_0B-lREOCs4iRqETlHUUYhCN1H2e_QO_iYiWbNvf0NkXpzRs590hLJTq47LZfNqb-CFXFPMpxo0CXhzJnTuPN1LzVf3bqxq_aYXb1hJPnUGqP4AGVdi1mP_1QdP6dBb3_ONoSOtQe4gM8sLnTma4tcbM9MlUIjZz-0YYSClphgm_xHegDOWZ1A=w640-h318" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">Fakta apa yang terjadi pada peristiwa tersebut? Jelaskan!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">Baca link berikut untuk memahami gambar: </div><h1 class="title ap-text-left ap-font-24-v2 ap-font-heading-v2 ap-font-20-v2 ap-text-darkgrey-v2 ap-pb-0 ap-px-0" style="background-color: white; box-sizing: border-box; color: #424a4c; font-family: poppins, sans-serif; line-height: 35px; margin-bottom: 0.5rem; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; width: 780.237px;"><span style="font-size: small;">👉<a href="https://akupintar.id/info-pintar/-/blogs/rangkaian-listrik-pengertian-rangkaian-rangkaian-paralel-rangkaian-seri-rumus-dan-penerapannya-" target="_blank">Rangkaian Listrik: Pengertian Rangkaian, Rangkaian Paralel, Rangkaian Seri, Rumus dan Penerapannya.</a></span></h1><div class="separator" style="clear: both; text-align: center;">=======================================================================</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgz98I92gL79OaZVSNP8hVzZweuddLDISysuphhwkVTVLlltblNqKsSraSExA8oW7AB4tzi-5ISjvBTuXRlBix4JV_gjM7NMlKYPOU2I0zYsxyQJcLLWus51mxc7NOWEyd1hvrTiXVgDXX27QQtIN6njQ6z0n0sEcAdty0DQaKzoECT6JtAROkNerDAs6c" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="382" data-original-width="1119" height="218" src="https://blogger.googleusercontent.com/img/a/AVvXsEgz98I92gL79OaZVSNP8hVzZweuddLDISysuphhwkVTVLlltblNqKsSraSExA8oW7AB4tzi-5ISjvBTuXRlBix4JV_gjM7NMlKYPOU2I0zYsxyQJcLLWus51mxc7NOWEyd1hvrTiXVgDXX27QQtIN6njQ6z0n0sEcAdty0DQaKzoECT6JtAROkNerDAs6c=w640-h218" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">Fakta apa yang terjadi pada peristiwa tersebut? 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Jelaskan!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;">Baca link berikut untuk memahami gambar: </div><h1 class="title ap-text-left ap-font-24-v2 ap-font-heading-v2 ap-font-20-v2 ap-text-darkgrey-v2 ap-pb-0 ap-px-0" style="background-color: white; box-sizing: border-box; color: #424a4c; font-family: poppins, sans-serif; line-height: 35px; margin-bottom: 0.5rem; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; width: 780.237px;"><span style="font-size: small;">👉<a href="https://kumparan.com/berita-hari-ini/cara-membaca-amperemeter-lengkap-dengan-contoh-soalnya-sebagai-panduan-1xY4gkHdhHv/2" target="_blank">Cara Membaca Amperemeter Lengkap dengan Contoh Soalnya sebagai Panduan</a></span></h1></div><div class="separator" style="clear: both; text-align: center;">=======================================================================</div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhMV0rLj4POi3vC-XSHZy-AN8nGRM-GvukCJP27-PGyvbRjrLP-hY6ebZR-g2GOo5eo_N3wwdLFNQpKOrTg18Vmc4Pw8E-BinRQoLRNZlvk6BFfwVrkWdx59715VV5p-XbjpheTMJVRfnCJ9wW0EgwZRrD6XWwz-pkSraBP0k5H2MNsDEakp_WFiot5ez8" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="432" data-original-width="885" height="312" src="https://blogger.googleusercontent.com/img/a/AVvXsEhMV0rLj4POi3vC-XSHZy-AN8nGRM-GvukCJP27-PGyvbRjrLP-hY6ebZR-g2GOo5eo_N3wwdLFNQpKOrTg18Vmc4Pw8E-BinRQoLRNZlvk6BFfwVrkWdx59715VV5p-XbjpheTMJVRfnCJ9wW0EgwZRrD6XWwz-pkSraBP0k5H2MNsDEakp_WFiot5ez8=w640-h312" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">Fakta apa yang terjadi pada peristiwa tersebut? Jelaskan!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">Baca link berikut untuk memahami gambar: </div><h1 class="title ap-text-left ap-font-24-v2 ap-font-heading-v2 ap-font-20-v2 ap-text-darkgrey-v2 ap-pb-0 ap-px-0" style="background-color: white; box-sizing: border-box; color: #424a4c; font-family: poppins, sans-serif; line-height: 35px; margin-bottom: 0.5rem; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; text-align: left; width: 780.237px;"><span style="font-size: small;">👉<a href="https://www.quipper.com/id/blog/mapel/fisika/hukum-kirchoff/" target="_blank">Penjelasan Hukum Kirchoff 1 dan 2 Lengkap dengan Bunyi, Rumus dan Kegunaannya</a></span></h1><div class="separator" style="clear: both; text-align: center;">=======================================================================</div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhtLLgC57UGCZ6a3Dc9Dl6DATanQ_H1gbgl8MShx8SuaRg7yaeMHo2L29dCaLU1rAdlfpL54Ax_syGnSykY8V0sn1sIOH2DMh3w7emb5yIwVuLO7-Y0lFZy5npcY4nGHVJh_Wjyrs8XzvThnJIBY7faOuaGeTEkkYs_RINNFwg0bC5SpplSrrmD64iMDW4" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="536" data-original-width="605" height="567" src="https://blogger.googleusercontent.com/img/a/AVvXsEhtLLgC57UGCZ6a3Dc9Dl6DATanQ_H1gbgl8MShx8SuaRg7yaeMHo2L29dCaLU1rAdlfpL54Ax_syGnSykY8V0sn1sIOH2DMh3w7emb5yIwVuLO7-Y0lFZy5npcY4nGHVJh_Wjyrs8XzvThnJIBY7faOuaGeTEkkYs_RINNFwg0bC5SpplSrrmD64iMDW4=w640-h567" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">Fakta apa yang terjadi pada peristiwa tersebut? Jelaskan!</div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Baca link berikut untuk memahami gambar: </div><h1 class="title ap-text-left ap-font-24-v2 ap-font-heading-v2 ap-font-20-v2 ap-text-darkgrey-v2 ap-pb-0 ap-px-0" style="background-color: white; box-sizing: border-box; color: #424a4c; font-family: poppins, sans-serif; line-height: 35px; margin-bottom: 0.5rem; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; width: 780.237px;"><span style="font-size: small;">👉<a href="https://fisikamemangasyik.wordpress.com/fisika-1/listrik/rfcfc/hukum-ii-kirchhoff/" target="_blank">Hukum II Kirchhoff</a></span></h1></div><div class="separator" style="clear: both; text-align: center;">=======================================================================</div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiLzzY9lb-ivfOMhbhixCXbXw61_MK47b26JAUBlZLWuQwGVLpP2BHzVAmrY9OqPpSl-E9R-_rPV2W8TxoIv60iyx0lH6DM3UQXLW1D_sHShUyl3hfxlcDLzDkdvFBsxFO6lHprtnrDyvvqok2axWGVRQ4x88eX0ws5mB9xVc34UyWobvc-D7GJkk2bYzM" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="351" data-original-width="977" height="230" src="https://blogger.googleusercontent.com/img/a/AVvXsEiLzzY9lb-ivfOMhbhixCXbXw61_MK47b26JAUBlZLWuQwGVLpP2BHzVAmrY9OqPpSl-E9R-_rPV2W8TxoIv60iyx0lH6DM3UQXLW1D_sHShUyl3hfxlcDLzDkdvFBsxFO6lHprtnrDyvvqok2axWGVRQ4x88eX0ws5mB9xVc34UyWobvc-D7GJkk2bYzM=w640-h230" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">Fakta apa yang terjadi pada peristiwa tersebut? Jelaskan!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;">Baca link berikut untuk memahami gambar: </div><h1 class="title ap-text-left ap-font-24-v2 ap-font-heading-v2 ap-font-20-v2 ap-text-darkgrey-v2 ap-pb-0 ap-px-0" style="background-color: white; box-sizing: border-box; color: #424a4c; font-family: poppins, sans-serif; line-height: 35px; margin-bottom: 0.5rem; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; width: 780.237px;"><span style="font-size: small;">👉<a href="https://www.tukang-listrik.com/2021/04/pengertian-dan-fenomena-listrik-statis.html" style="box-sizing: border-box; color: #333333; display: inline; font-family: Mukta, sans-serif; letter-spacing: 0.2px; margin: 20px 0px; padding: 0px; text-align: center; text-decoration-line: none; transition: all 400ms ease-in-out 0s;" target="_blank">Pengertian dan Fenomena Listrik Statis dalam Kehidupan Sehari-hari</a></span></h1></div><div class="separator" style="clear: both; text-align: center;">=======================================================================</div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEibiVNRAPwfgfep-JFLBZTKuM9f6q1kiBhduf0aD2JJjWtgZOdWdoa8rnnOkEjFevk0YRa_owvAYxEtG8bvrhJSrzR9F4xCksKHqM_Yq_Bh3DDlVtU7MrTk0_wK-rzlr5PQa-6kVurc2vX1KySLvsvdswHJtg6TmbQbYKH1TnFFlWPB_zC4uD16XduzLb0" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="425" data-original-width="604" height="450" src="https://blogger.googleusercontent.com/img/a/AVvXsEibiVNRAPwfgfep-JFLBZTKuM9f6q1kiBhduf0aD2JJjWtgZOdWdoa8rnnOkEjFevk0YRa_owvAYxEtG8bvrhJSrzR9F4xCksKHqM_Yq_Bh3DDlVtU7MrTk0_wK-rzlr5PQa-6kVurc2vX1KySLvsvdswHJtg6TmbQbYKH1TnFFlWPB_zC4uD16XduzLb0=w640-h450" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">Fakta apa yang terjadi pada peristiwa tersebut? Jelaskan!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;">Baca link berikut untuk memahami gambar: </div><h1 class="title ap-text-left ap-font-24-v2 ap-font-heading-v2 ap-font-20-v2 ap-text-darkgrey-v2 ap-pb-0 ap-px-0" style="background-color: white; box-sizing: border-box; color: #424a4c; font-family: poppins, sans-serif; line-height: 35px; margin-bottom: 0.5rem; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; width: 780.237px;"><span style="font-size: small;">👉<a href="https://www.ruangguru.com/blog/pengertian-hukum-coulomb" target="_blank">Hukum Coulomb: Pengertian, Rumus, dan Contoh Soal | Fisika Kelas 12</a></span></h1></div><div class="separator" style="clear: both; text-align: center;">=======================================================================</div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiBrecq97k0ua2BhXWouIJG64JHwhDAbgz-ZAxEnvHA18VpTiljUPXlAF048lZOkdgtW6bghHRklKwpJ9wU1bY82nwvReUzMP1HUihR9JuCrQOil9I0UbuZNSPXYr3iVrZIJlX8Cl0BvdmaVs5G2VNfUb1VE1vgnGVmU_fGf6F2fGrXvlV72cPYeZKBRXU" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="468" data-original-width="1504" height="200" src="https://blogger.googleusercontent.com/img/a/AVvXsEiBrecq97k0ua2BhXWouIJG64JHwhDAbgz-ZAxEnvHA18VpTiljUPXlAF048lZOkdgtW6bghHRklKwpJ9wU1bY82nwvReUzMP1HUihR9JuCrQOil9I0UbuZNSPXYr3iVrZIJlX8Cl0BvdmaVs5G2VNfUb1VE1vgnGVmU_fGf6F2fGrXvlV72cPYeZKBRXU=w640-h200" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">Fakta apa yang terjadi pada peristiwa tersebut? Jelaskan!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;">Baca link berikut untuk memahami gambar: </div><h1 class="title ap-text-left ap-font-24-v2 ap-font-heading-v2 ap-font-20-v2 ap-text-darkgrey-v2 ap-pb-0 ap-px-0" style="background-color: white; box-sizing: border-box; color: #424a4c; font-family: poppins, sans-serif; line-height: 35px; margin-bottom: 0.5rem; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; width: 780.237px;"><span style="font-size: small;">👉<a href="https://www.liputan6.com/hot/read/4105243/jenis-jenis-kapasitor-beserta-gambarnya-komponen-elektronika-penting?page=3" target="_blank">Jenis-Jenis Kapasitor Beserta Gambarnya, Komponen Elektronika Penting</a></span></h1></div><div class="separator" style="clear: both; text-align: center;">=======================================================================</div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj0B-5jOnyOOeYjkBxjIdIpjbXvW_XnvCSMPW-HqhijbHsELe64XOY-lwhJo5jTWbdbRXM5no7F__Tz93RKfGFQyfbD157IPDk7zP0eVICZJCrhh8P2Plux0uDB_RyCVyLAPSNr0FxIk8IH7IK5F_4m6gCsuqAVb1SY0ip775xMIK1g3lDTU1I6HAAz3vg" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="657" data-original-width="1032" height="408" src="https://blogger.googleusercontent.com/img/a/AVvXsEj0B-5jOnyOOeYjkBxjIdIpjbXvW_XnvCSMPW-HqhijbHsELe64XOY-lwhJo5jTWbdbRXM5no7F__Tz93RKfGFQyfbD157IPDk7zP0eVICZJCrhh8P2Plux0uDB_RyCVyLAPSNr0FxIk8IH7IK5F_4m6gCsuqAVb1SY0ip775xMIK1g3lDTU1I6HAAz3vg=w640-h408" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">Fakta apa yang terjadi pada peristiwa tersebut? Jelaskan!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;">Baca link berikut untuk memahami gambar: </div><h1 class="title ap-text-left ap-font-24-v2 ap-font-heading-v2 ap-font-20-v2 ap-text-darkgrey-v2 ap-pb-0 ap-px-0" style="background-color: white; box-sizing: border-box; color: #424a4c; font-family: poppins, sans-serif; line-height: 35px; margin-bottom: 0.5rem; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; width: 780.237px;"><span style="font-size: small;">👉<a href="https://ilmupedia105.blogspot.com/2018/07/lengkap-prinsip-cara-kerja-generator.html" target="_blank">Prinsip Cara Kerja Generator Dalam Menghasilkan Listrik</a></span></h1></div><div class="separator" style="clear: both; text-align: center;">=======================================================================</div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgstK7lGQKAsulxTnZrIbi9SPIhPfvvNnM0NgJxfDK5E2cMw_BS155gECYeDWdxXjAmydsdrIWdlQxO7MVHvClleocAvcPKx0EZj5QrIe2mF5_7p-uBE3SGZhPb3jlWfS7hFNmx6hp9IHnafcIKerQRqwktsBEHo1JhUXpVGD9IRYoRQJVP0AFzbkMcPtA" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="602" data-original-width="778" height="495" src="https://blogger.googleusercontent.com/img/a/AVvXsEgstK7lGQKAsulxTnZrIbi9SPIhPfvvNnM0NgJxfDK5E2cMw_BS155gECYeDWdxXjAmydsdrIWdlQxO7MVHvClleocAvcPKx0EZj5QrIe2mF5_7p-uBE3SGZhPb3jlWfS7hFNmx6hp9IHnafcIKerQRqwktsBEHo1JhUXpVGD9IRYoRQJVP0AFzbkMcPtA=w640-h495" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">Fakta apa yang terjadi pada peristiwa tersebut? Jelaskan!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;">Baca link berikut untuk memahami gambar: </div><h1 class="title ap-text-left ap-font-24-v2 ap-font-heading-v2 ap-font-20-v2 ap-text-darkgrey-v2 ap-pb-0 ap-px-0" style="background-color: white; box-sizing: border-box; color: #424a4c; font-family: poppins, sans-serif; line-height: 35px; margin-bottom: 0.5rem; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; width: 780.237px;"><span style="font-size: small;">👉<a href="https://solusiindustri.com/fungsi-dan-berbagai-macam-jenis-trafo/" target="_blank">Fungsi dan Berbagai Macam Jenis Trafo</a></span></h1><div><h1 class="entry-title" itemprop="headline" style="background-color: white; border: 0px; box-sizing: inherit; font-family: Montserrat, sans-serif; line-height: 1.2em; margin: 0px; padding: 0px;"><span style="color: #424a4c; font-family: poppins, sans-serif; font-size: medium;">👉</span><span style="font-size: small;"><a href="https://thecityfoundry.com/transformator/" target="_blank">Transformator: Gambar, Fungsi, Prinsip Kerja, Jenis Rumus</a></span></h1></div></div></div></div></div></div></div></div></div></div></div><p></p>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8185710560472973854.post-21406009117412327512023-11-19T17:45:00.006+07:002023-11-21T07:01:08.240+07:00Kisi-kisi Soal PAS Fisika Kelas 11<p> <b> </b></p><div class="separator" style="clear: both; text-align: center;"><b><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj4pZTjl21YhWnsG04Z4l0QQiWCfAifu_Jmjw-C8c6mwIab1Ni64FOMPtmwH38Pvzo6f_PQag8ehIN95JDOzIvj4-3ke8qoMwnsyudyCWDYVeiTD-78ad8-KxhO2E14kvn7tqMvD2ll83Btr1rvX-BwNmTx9GsiK-He_j5Yxe9ajNLmVx3e8QXDzISd_1c" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1355" data-original-width="2406" src="https://blogger.googleusercontent.com/img/a/AVvXsEj4pZTjl21YhWnsG04Z4l0QQiWCfAifu_Jmjw-C8c6mwIab1Ni64FOMPtmwH38Pvzo6f_PQag8ehIN95JDOzIvj4-3ke8qoMwnsyudyCWDYVeiTD-78ad8-KxhO2E14kvn7tqMvD2ll83Btr1rvX-BwNmTx9GsiK-He_j5Yxe9ajNLmVx3e8QXDzISd_1c=s16000" /></a></b></div><div><span data-canva-clipboard="{ " a " : 5 , " d " : " B " , " h " : " w w w . c a n v a . c o m " , " c " : " D A F 0 v x r E Y _ U " , " i " : " G 3 O K y S I B 8 A V 9 i 9 w T 6 7 u m 8 A " , " b " : 1 7 0 0 5 2 4 8 4 1 1 2 6 , " A ? " : " E " , " A " : { " A " : [ { " A " : { " A ? " : " A " , " A " : " B a g i   m e r e k a   y a n g   s e d a n g   m e m p e r s i a p k a n   d i r i   u n t u k   P A S   F i s i k a   X I ,   a r t i k e l   i n i   a k a n   m e n j a d i   s u m b e r   d a y a   y a n g   b e r h a r g a .   K a m i   a k a n   m e m b a h a s   b e b e r a p a   k o n s e p   d a n   i s t i l a h   p e n t i n g   y a n g   m u n g k i n   m u n c u l   d a l a m   u j i a n   A n d a .   D e n g a n   m e m a h a m i   k o n s e p - k o n s e p   i n i ,   A n d a   a k a n   d a p a t   m e n a v i g a s i   p e r t a n y a a n   u j i a n   d e n g a n   l e b i h   b a i k   d a n   m e n i n g k a t k a n   s k o r   A n d a . \ n " } , " B " : { " A " : " Y A F d J t 8 d A Y 0 , 0 " } } , { " A " : { " A ? " : " A " , " A " : " D i n a m i k a   R o t a s i \ n " } , " B " : { " B " : " 2 4 p x " } } , { " A " : { " A ? " : " A " , " A " : " D i n a m i k a   r o t a s i   a d a l a h   c a b a n g   d a r i   f i s i k a   y a n g   m e n g k a j i   t e n t a n g   g e r a k a n   b e n d a   y a n g   b e r p u t a r .   D u a   k o n s e p   p e n t i n g   d a l a m   d i n a m i k a   r o t a s i   a d a l a h   m o m e n   g a y a   d a n   m o m e n   i n e r s i a . \ n " } , " C " : { " B " : t r u e } } , { " A " : { " A ? " : " A " , " A " : " M o m e n   G a y a \ n " } , " B " : { " B " : " 1 8 . 7 2 p x " } } , { " A " : { " A ? " : " A " , " A " : " M o m e n   g a y a   a d a l a h   k o n s e p   d a s a r   d a l a m   f i s i k a   y a n g   m e n j e l a s k a n   b a g a i m a n a   g a y a   d a p a t   m e n y e b a b k a n   o b y e k   b e r p u t a r .   M o m e n   g a y a   d a p a t   d i h i t u n g   d e n g a n   m e n g a l i k a n   g a y a   y a n g   d i t e r a p k a n   d e n g a n   j a r a k   d a r i   t i t i k   p u t a r   k e   t i t i k   d i   m a n a   g a y a   d i t e r a p k a n . \ n " } , " C " : { " B " : t r u e } } , { " A " : { " A ? " : " A " , " A " : " M o m e n   I n e r s i a \ n " } , " B " : { " B " : " 1 8 . 7 2 p x " } } , { " A " : { " A ? " : " A " , " A " : " M o m e n   i n e r s i a   a d a l a h   u k u r a n   r e s i s t a n s i   s u a t u   o b j e k   t e r h a d a p   p e r u b a h a n   k e c e p a t a n   r o t a s i n y a .   I n i   s a n g a t   p e n t i n g   d a l a m   p e r i s t i w a   f i s i k a   s e p e r t i   l a n d i n g ,   t a k e   o f f ,   d a n   t e r b a n g . \ n " } , " C " : { " B " : t r u e } } , { " A " : { " A ? " : " A " , " A " : " H u k u m   H o o k   d a n   K o n s t a n t a   E l a s t i s i t a s   P e g a s \ n " } , " B " : { " B " : " 2 4 p x " } } , { " A " : { " A ? " : " A " , " A " : " H u k u m   H o o k   a d a l a h   p r i n s i p   f i s i k a   y a n g   m e n j e l a s k a n   b a g a i m a n a   p e g a s   d a n   o b j e k   e l a s t i s   l a i n n y a   b e r p e r i l a k u .   H u k u m   i n i   m e n y a t a k a n   b a h w a   g a y a   y a n g   d i t e r a p k a n   p a d a   p e g a s   s e c a r a   l a n g s u n g   p r o p o r s i o n a l   d e n g a n   p e r u b a h a n   p a n j a n g n y a .   K o n s t a n t a   e l a s t i s i t a s   p e g a s   a d a l a h   u k u r a n   s e j a u h   m a n a   p e g a s   d a p a t   d i s t r e t c h   a t a u   d i k o m p r e s i . \ n " } , " C " : { " B " : t r u e } } , { " A " : { " A ? " : " A " , " A " : " S u s u n a n   P e g a s \ n " } , " B " : { " B " : " 1 8 . 7 2 p x " } } , { " A " : { " A ? " : " A " , " A " : " B a g a i m a n a   p e g a s   d i a t u r   d a p a t   m e m p e n g a r u h i   b a g a i m a n a   m e r e k a   b e r p e r i l a k u .   M i s a l n y a ,   p e g a s   y a n g   d i s u s u n   s e c a r a   p a r a l e l   a k a n   m e m i l i k i   k o n s t a n t a   e l a s t i s i t a s   t o t a l   y a n g   s a m a   d e n g a n   j u m l a h   k o n s t a n t a   e l a s t i s i t a s   m a s i n g - m a s i n g   p e g a s . \ n " } , " C " : { " B " : t r u e } } , { " A " : { " A ? " : " A " , " A " : " T i t i k   B e r a t   d a n   P e r i s t i w a   F i s i k a \ n " } , " B " : { " B " : " 2 4 p x " } } , { " A " : { " A ? " : " A " , " A " : " T i t i k   b e r a t   a d a l a h   k o n s e p   l a i n   y a n g   s a n g a t   p e n t i n g   d a l a m   f i s i k a .   I n i   a d a l a h   t i t i k   d i   m a n a   b e r a t   t o t a l   s u a t u   o b j e k   d a p a t   d i a n g g a p   t e r k o n s e n t r a s i .   M i s a l n y a ,   t i t i k   b e r a t   b i d a n g   s e g i t i g a   d a p a t   d i h i t u n g   m e n g g u n a k a n   b e r b a g a i   m e t o d e ,   t e r g a n t u n g   p a d a   b e n t u k   d a n   u k u r a n   s e g i t i g a . \ n " } , " C " : { " B " : t r u e } } , { " A " : { " A ? " : " A " , " A " : " C a r a   K e r j a ,   A l a t   d a n   B a h a n \ n " } , " B " : { " B " : " 2 4 p x " } } , { " A " : { " A ? " : " A " , " A " : " M e m a h a m i   k o n s e p   f i s i k a   j u g a   b e r a r t i   m e m a h a m i   c a r a   k e r j a   a l a t   d a n   b a h a n   y a n g   d i g u n a k a n   d a l a m   e k s p e r i m e n   f i s i k a .   A l a t   d a n   b a h a n   d a p a t   m e m a n f a a t k a n   h u k u m   d a n   p r i n s i p   f i s i k a   u n t u k   m e n c a p a i   t u j u a n   t e r t e n t u ,   s e p e r t i   m e n g u k u r   m o m e n   i n e r s i a   a t a u   m e n g u j i   h u k u m   H o o k . \ n J a d i ,   j i k a   A n d a   m e m p e r s i a p k a n   d i r i   u n t u k   P A S   F i s i k a   X I ,   p a s t i k a n   u n t u k   m e m a h a m i   k o n s e p - k o n s e p   i n i   d e n g a n   b a i k .   S e m o g a   s u k s e s ! " } , " C " : { " B " : t r u e } } ] } } "></span><div style="direction: ltr; line-height: 1.4; margin-left: 0px;"><p><span style="font-size: 16px; letter-spacing: 0em;">Bagi mereka yang sedang mempersiapkan diri untuk PAS Fisika XI, artikel ini akan menjadi sumber daya yang berharga. Kami akan membahas beberapa konsep dan istilah penting yang mungkin muncul dalam ujian Anda. Dengan memahami konsep-konsep ini, Anda akan dapat menavigasi pertanyaan ujian dengan lebih baik dan meningkatkan skor Anda.</span></p></div><div style="direction: ltr; line-height: 1.4; margin-left: 0px;"><p><span style="font-size: 24px; letter-spacing: 0em;">Dinamika Rotasi</span></p></div><div style="direction: ltr; line-height: 1.4; margin-left: 0px;"><p><span style="font-size: 16px; letter-spacing: 0em;">Dinamika rotasi adalah cabang dari fisika yang mengkaji tentang gerakan benda yang berputar. Dua konsep penting dalam dinamika rotasi adalah momen gaya dan momen inersia.</span></p></div><div style="direction: ltr; line-height: 1.4; margin-left: 0px;"><p><span style="font-size: 18.72px; letter-spacing: 0em;">Momen Gaya</span></p></div><div style="direction: ltr; line-height: 1.4; margin-left: 0px;"><p><span style="font-size: 16px; letter-spacing: 0em;">Momen gaya adalah konsep dasar dalam fisika yang menjelaskan bagaimana gaya dapat menyebabkan obyek berputar. Momen gaya dapat dihitung dengan mengalikan gaya yang diterapkan dengan jarak dari titik putar ke titik di mana gaya diterapkan.</span></p></div><div style="direction: ltr; line-height: 1.4; margin-left: 0px;"><p><span style="font-size: 18.72px; letter-spacing: 0em;">Momen Inersia</span></p></div><div style="direction: ltr; line-height: 1.4; margin-left: 0px;"><p><span style="font-size: 16px; letter-spacing: 0em;">Momen inersia adalah ukuran resistansi suatu objek terhadap perubahan kecepatan rotasinya. Ini sangat penting dalam peristiwa fisika seperti landing, take off, dan terbang.</span></p></div><div style="direction: ltr; line-height: 1.4; margin-left: 0px;"><p><span style="font-size: 24px; letter-spacing: 0em;">Hukum Hook dan Konstanta Elastisitas Pegas</span></p></div><div style="direction: ltr; line-height: 1.4; margin-left: 0px;"><p><span style="font-size: 16px; letter-spacing: 0em;">Hukum Hook adalah prinsip fisika yang menjelaskan bagaimana pegas dan objek elastis lainnya berperilaku. Hukum ini menyatakan bahwa gaya yang diterapkan pada pegas secara langsung proporsional dengan perubahan panjangnya. Konstanta elastisitas pegas adalah ukuran sejauh mana pegas dapat distretch atau dikompresi.</span></p></div><div style="direction: ltr; line-height: 1.4; margin-left: 0px;"><p><span style="font-size: 18.72px; letter-spacing: 0em;">Susunan Pegas</span></p></div><div style="direction: ltr; line-height: 1.4; margin-left: 0px;"><p><span style="font-size: 16px; letter-spacing: 0em;">Bagaimana pegas diatur dapat mempengaruhi bagaimana mereka berperilaku. Misalnya, pegas yang disusun secara paralel akan memiliki konstanta elastisitas total yang sama dengan jumlah konstanta elastisitas masing-masing pegas.</span></p></div><div style="direction: ltr; line-height: 1.4; margin-left: 0px;"><p><span style="font-size: 24px; letter-spacing: 0em;">Titik Berat dan Peristiwa Fisika</span></p></div><div style="direction: ltr; line-height: 1.4; margin-left: 0px;"><p><span style="font-size: 16px; letter-spacing: 0em;">Titik berat adalah konsep lain yang sangat penting dalam fisika. Ini adalah titik di mana berat total suatu objek dapat dianggap terkonsentrasi. Misalnya, titik berat bidang segitiga dapat dihitung menggunakan berbagai metode, tergantung pada bentuk dan ukuran segitiga.</span></p></div><div style="direction: ltr; line-height: 1.4; margin-left: 0px;"><p><span style="font-size: 24px; letter-spacing: 0em;">Cara Kerja, Alat dan Bahan</span></p></div><div style="direction: ltr; line-height: 1.4; margin-left: 0px;"><p><span style="font-size: 16px; letter-spacing: 0em;">Memahami konsep fisika juga berarti memahami cara kerja alat dan bahan yang digunakan dalam eksperimen fisika. Alat dan bahan dapat memanfaatkan hukum dan prinsip fisika untuk mencapai tujuan tertentu, seperti mengukur momen inersia atau menguji hukum Hook.</span></p></div><div style="direction: ltr; line-height: 1.4; margin-left: 0px;"><p><span style="font-size: 16px; letter-spacing: 0em;">Jadi, jika Anda mempersiapkan diri untuk PAS Fisika XI, pastikan untuk memahami konsep-konsep ini dengan baik. Semoga sukses!</span></p></div></div><p></p><p><b>Soal nomor 1: Cermati gambar berikut!</b></p><p><br /></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEioq5qRMd2xrg9_VSuE07inW49vyyyAMSxK5_cVlmX8KfPOyycCx1oSx3XU3mSv7Eovmqkd-6yrsMApC5jUwKiSpPeW-iB1t760reLyzImFkyv-0IpBme_kf3a09kitnBRfSC3RqErY0xDzIlQDksuG-6W1Zhmo5CIhAmw9yEmKsTpy5q5NE2faLLhCJJM" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="686" data-original-width="1012" height="434" src="https://blogger.googleusercontent.com/img/a/AVvXsEioq5qRMd2xrg9_VSuE07inW49vyyyAMSxK5_cVlmX8KfPOyycCx1oSx3XU3mSv7Eovmqkd-6yrsMApC5jUwKiSpPeW-iB1t760reLyzImFkyv-0IpBme_kf3a09kitnBRfSC3RqErY0xDzIlQDksuG-6W1Zhmo5CIhAmw9yEmKsTpy5q5NE2faLLhCJJM=w640-h434" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><br /></td></tr></tbody></table><p>Ceritakan peristiwa fisika apa saja yang terjadi! Kaitkan peristiwa yang terjadi dengan momen gaya, momen inersia, dan dinamika rotasi. Apa saja kata-kata penting yang menentukan peristiwa momen gaya, momen inersia, dan dinamika rotasi dapat terjadi? Tuliskan dan jelaskan kata-kata penting yang anda maksud!<br /><br /></p><p></p><p><b>Soal nomor 2: Cermati gambar berikut!</b></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh0kIuUZfqP2GBrMVZZSf3tpvVGkPz_EU8DUQJh4KiUii_UeYEETpHHE6crS0nR-vj9YClBLKSQqCMwHA-KawHez7jSTelQF_w2oJ0dk2wloHTUYWyPEAro4gsltZz7dLb9JtW5auAef8pm3nZ_sdM89x7z7DWbdrj6BRtxJbpDSjiYD1Sm1aiMPIcJz9A" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="404" data-original-width="328" height="640" src="https://blogger.googleusercontent.com/img/a/AVvXsEh0kIuUZfqP2GBrMVZZSf3tpvVGkPz_EU8DUQJh4KiUii_UeYEETpHHE6crS0nR-vj9YClBLKSQqCMwHA-KawHez7jSTelQF_w2oJ0dk2wloHTUYWyPEAro4gsltZz7dLb9JtW5auAef8pm3nZ_sdM89x7z7DWbdrj6BRtxJbpDSjiYD1Sm1aiMPIcJz9A=w520-h640" width="520" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both;">Ceritakan peristiwa fisika apa saja yang terjadi! Kaitkan peristiwa yang terjadi dengan momen gaya, momen inersia, dan dinamika rotasi. Apa saja kata-kata penting yang menentukan peristiwa momen gaya, momen inersia, dan dinamika rotasi dapat terjadi? Tuliskan dan jelaskan kata-kata penting yang anda maksud!</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><b>Soal nomor 3: Cermati gambar berikut!</b></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiE33O83wemKbKUQqGvOJfo65pPzeUXb4GChMNQZV0o2UpFV-0XEPdxjsfnHXS8GCHQK-HKd8LddJqe5hibGYSr2pUYL1y1wgDOAnaT3ujvGZTEK-11R05NHMlnzE98HajwFJbdr5U2jtFRPHDmVou_7Zo5y9qxv_khtnNkkT4l1s93KIDTzwIafeJO6rs" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="666" data-original-width="910" height="468" src="https://blogger.googleusercontent.com/img/a/AVvXsEiE33O83wemKbKUQqGvOJfo65pPzeUXb4GChMNQZV0o2UpFV-0XEPdxjsfnHXS8GCHQK-HKd8LddJqe5hibGYSr2pUYL1y1wgDOAnaT3ujvGZTEK-11R05NHMlnzE98HajwFJbdr5U2jtFRPHDmVou_7Zo5y9qxv_khtnNkkT4l1s93KIDTzwIafeJO6rs=w640-h468" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both;">Gerakan seperti apa saja yang dapat terjadi dari gambar 1 s.d. 12! Mengapa gerakan-gerakan itu bisa dilakukan? Jelaskan!</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Soal nomor 4: <b>Cermati gambar berikut!</b></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh4P6gf-RR1fLnRvyJHRN7fS5E8lbXuuV6lwF7fg-M_HWfRIXMIH24T_FLf6JQYRZBprtq0-miDolI73U3xFWz19wVVacIGuCdWIpXrEzF7vudKaexA1jmOzj-JXeykC4LAbdHS6IIpkQmeATE1H7-1dVlJkiWtUuk7pW-Mni7GKJ3rU4InIZ85EtWxQyI" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="873" data-original-width="903" height="619" src="https://blogger.googleusercontent.com/img/a/AVvXsEh4P6gf-RR1fLnRvyJHRN7fS5E8lbXuuV6lwF7fg-M_HWfRIXMIH24T_FLf6JQYRZBprtq0-miDolI73U3xFWz19wVVacIGuCdWIpXrEzF7vudKaexA1jmOzj-JXeykC4LAbdHS6IIpkQmeATE1H7-1dVlJkiWtUuk7pW-Mni7GKJ3rU4InIZ85EtWxQyI=w640-h619" width="640" /></a></div><div class="separator" style="clear: both;"><br /></div>Kelompokkan gerakan-gerakan menjadi kelompok-kelompok gerakan yang relatif sama. Apa yang menjadi dasar anda mengelompokkannya menjadi kelompok-kelompok yang sama? Jelaskan!</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Soal nomor 5: <b>Cermati gambar berikut!</b></div><div class="separator" style="clear: both;"><b><br /></b></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhIZ2Rd5ZQCT4Iag10xUI-713SJ3WQMTTLyrwX2QNqVBg3bJjnI9TX8zg09GjTaPJlqeePSy9elUcfTjX5pwNjMmnxZmtzlZg1KvZVJjZSU9CDgeu08DyXFYhgIL3DTo2lOWhcMMd8LWP4lF7XSMCccu1Y0ejqQVUIlguuFUhVZSF0582vzW7-lGD3JNt0" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="419" data-original-width="659" height="203" src="https://blogger.googleusercontent.com/img/a/AVvXsEhIZ2Rd5ZQCT4Iag10xUI-713SJ3WQMTTLyrwX2QNqVBg3bJjnI9TX8zg09GjTaPJlqeePSy9elUcfTjX5pwNjMmnxZmtzlZg1KvZVJjZSU9CDgeu08DyXFYhgIL3DTo2lOWhcMMd8LWP4lF7XSMCccu1Y0ejqQVUIlguuFUhVZSF0582vzW7-lGD3JNt0" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both;">Jelaskan perbedaan kedua gambar! Kaitkan kedua gambar dengan konstanta elastisitas pegas dan Hukum Hook!</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Soal nomor 6: <b>Cermati gambar berikut!</b></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiqpQTw-SGK_4VsOt-HVC1iqspAEUdR9ebP_lnntJqJtD9n0vp6uHYR25erQsgkTHNqnnqe3QZseHIMkENWU_JgVp76D7ndsyJS6f83B443U2zQaYUj357flQkYqerDJNVk7H2xWtwXNZauKY8HevNMTW2NtI5pKY9bWSYgwaM-9aR-h9T_RsjC10mY2lk" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="422" data-original-width="735" height="184" src="https://blogger.googleusercontent.com/img/a/AVvXsEiqpQTw-SGK_4VsOt-HVC1iqspAEUdR9ebP_lnntJqJtD9n0vp6uHYR25erQsgkTHNqnnqe3QZseHIMkENWU_JgVp76D7ndsyJS6f83B443U2zQaYUj357flQkYqerDJNVk7H2xWtwXNZauKY8HevNMTW2NtI5pKY9bWSYgwaM-9aR-h9T_RsjC10mY2lk" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;">Jelaskan perbedaan kedua gambar! Kaitkan kedua gambar dengan konstanta elastisitas pegas dan Hukum Hook!</span></div><br />Soal nomor 7: <b>Cermati gambar berikut!</b></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiBmhd-WN1vB_KfuozSqUxv-K5HYSvrTWNq2pzrO2snpkXHur9L1LIbtT_0ZOUA-rVWxmeuNYN4MwuWmDjgdHkmU5JEz332AeLfBq8lCyo55Q1EEJQalIHotVr1fWMuYw2rfd48WKiyQdNLxZHto-fQJ4ja-HsoJVxFJ8SQlNZzQRZd8sv49wwi9TQEUhM" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="415" data-original-width="533" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEiBmhd-WN1vB_KfuozSqUxv-K5HYSvrTWNq2pzrO2snpkXHur9L1LIbtT_0ZOUA-rVWxmeuNYN4MwuWmDjgdHkmU5JEz332AeLfBq8lCyo55Q1EEJQalIHotVr1fWMuYw2rfd48WKiyQdNLxZHto-fQJ4ja-HsoJVxFJ8SQlNZzQRZd8sv49wwi9TQEUhM" width="308" /></a></div><div class="separator" style="clear: both;"><br /></div>Ceritakan peristiwa yang terjadi! </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Soal nomor 8: </div><div class="separator" style="clear: both;"><a href="https://media-public.colearn.id/images/questions/F0800581P057.jpg" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="514" data-original-width="800" height="411" src="https://media-public.colearn.id/images/questions/F0800581P057.jpg" width="640" /></a></div><br />Soal nomor 9: <b>Cermati gambar berikut!</b></div><div class="separator" style="clear: both;"><b><br /></b><a href="https://i.ytimg.com/vi/D_sWePtr_fA/maxresdefault.jpg" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="450" data-original-width="800" height="360" src="https://i.ytimg.com/vi/D_sWePtr_fA/maxresdefault.jpg" width="640" /></a></div><p></p><p>Bagaimana cara membuatnya? Jelaskan!</p><div><br /></div><div>Soal nomor 10: <b>Cermati gambar berikut!</b></div><div><b><br /></b></div><div><b><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjMkqtXME6GKFhmctZdcghqvXU4yf4v-atiORsoFWS9VK_h3wpJYTMpA3-vKV1QvqkJNr3VSMo9dsLpRlWFdyNCEUZGHBoKPHN4duboToNsDWGkzHjbUC7KhOn-0uCwQgeZF78f6n-Y2ynYPaXmDXHi6DiXVlU6Ub74cXmLtY2hxd2Hvkr_sf6ZJ8A333o" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="406" data-original-width="915" height="284" src="https://blogger.googleusercontent.com/img/a/AVvXsEjMkqtXME6GKFhmctZdcghqvXU4yf4v-atiORsoFWS9VK_h3wpJYTMpA3-vKV1QvqkJNr3VSMo9dsLpRlWFdyNCEUZGHBoKPHN4duboToNsDWGkzHjbUC7KhOn-0uCwQgeZF78f6n-Y2ynYPaXmDXHi6DiXVlU6Ub74cXmLtY2hxd2Hvkr_sf6ZJ8A333o=w640-h284" width="640" /></a></div><br />Mengapa pesawat bisa take off, terbang, dan landing?</b></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8185710560472973854.post-77334445718116504392023-11-19T09:39:00.018+07:002023-11-19T17:16:20.174+07:001.1 Notasi Ilmiah dan Pemanfaatannya Dalam Ilmu Fisika<p></p><div class="separator" style="clear: both; text-align: center;"><div style="clear: both; text-align: left;"><span style="font-size: medium;"><div class="separator" style="clear: both; text-align: center;"><a href="https://i0.wp.com/ahmaddahlan.net/wp-content/uploads/2022/07/template-1-1.jpg?fit=740%2C400&ssl=1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="740" height="346" src="https://i0.wp.com/ahmaddahlan.net/wp-content/uploads/2022/07/template-1-1.jpg?fit=740%2C400&ssl=1" width="640" /></a></div><br /><span><br /></span></span></div><div style="clear: both; text-align: left;"><span style="font-size: medium;"><span>Baca juga: <br /></span><span><span color="var(--theme-text-color)" face="Signika, Arial, sans-serif"><a href="https://prima.fisikasiswa.com/2023/11/bab-1-besaran.html" target="_blank">BAB 1.1 : PENGUKURAN PANJANG</a></span></span></span></div><div style="clear: both; text-align: left;"><span style="font-size: medium;"><span><br /></span></span></div><div style="clear: both; text-align: left;"><span style="font-size: medium;"><span><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgoTtZ-SlgZpFctn4xiIfEE9pqyhi_UuM9bwDhXhSi6nlGJSLaZm0X6vY7vaPDI8TbjjzejOuldCyBcfzsHKjU0pLfPMwtr5u7CEwvzX1F9vXg-UgIAuk-rkOZ9fvWQVqLerr2E0zflZc3C-08nJjQOhmSqV_coFSFwC67aUJaaXlOhgJx3Sbd0gqOUgZ8" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1072" data-original-width="1512" src="https://blogger.googleusercontent.com/img/a/AVvXsEgoTtZ-SlgZpFctn4xiIfEE9pqyhi_UuM9bwDhXhSi6nlGJSLaZm0X6vY7vaPDI8TbjjzejOuldCyBcfzsHKjU0pLfPMwtr5u7CEwvzX1F9vXg-UgIAuk-rkOZ9fvWQVqLerr2E0zflZc3C-08nJjQOhmSqV_coFSFwC67aUJaaXlOhgJx3Sbd0gqOUgZ8=s16000" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiFH7NKaL2BkNcLN3BaLL53djfsCrV4SCepECn8gFkpUPN-ufld-2tRCVIan1iChwcpW3HZPYC5E9vXSPKMuEzWmPFujbR55HOODfujENXruLqbKbTZ_PI78LrL_GST0hp-Djdy8CbHfT4t9QfHbWBs0kaBfGGOkhst_VITOOJaaYkpDJ0hMNdkHwfrBqU" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="952" data-original-width="1512" src="https://blogger.googleusercontent.com/img/a/AVvXsEiFH7NKaL2BkNcLN3BaLL53djfsCrV4SCepECn8gFkpUPN-ufld-2tRCVIan1iChwcpW3HZPYC5E9vXSPKMuEzWmPFujbR55HOODfujENXruLqbKbTZ_PI78LrL_GST0hp-Djdy8CbHfT4t9QfHbWBs0kaBfGGOkhst_VITOOJaaYkpDJ0hMNdkHwfrBqU=s16000" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiqW988Kguys38yCK-s8E4LkXrJFqzED7zhX--X4kZqpmeS9DkL5ufuItRLPLXWDUDAxFACB64GNSd7Yq9MkvJ3IZibJvUCOhrkiTdZ2NGPuOTSBFfJCM4023Rjdh5TxS-NLcum1KKIsoZBUnRDNiYhRxd0-5hcCY1XRheg-8QKw79ae9LjZ6mDi28L114" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="952" data-original-width="1512" src="https://blogger.googleusercontent.com/img/a/AVvXsEiqW988Kguys38yCK-s8E4LkXrJFqzED7zhX--X4kZqpmeS9DkL5ufuItRLPLXWDUDAxFACB64GNSd7Yq9MkvJ3IZibJvUCOhrkiTdZ2NGPuOTSBFfJCM4023Rjdh5TxS-NLcum1KKIsoZBUnRDNiYhRxd0-5hcCY1XRheg-8QKw79ae9LjZ6mDi28L114=s16000" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhIe-77B1wvgfJwbBi7QlsuWYhKJ7enYlT_Yl52RhNcAFJtCvI6bkBdHg9P1i75NLKX0uCDeZvlBlbWWFcThZfCygSgGQd3DwceXYsTjatk9jBTAfWdEhUj8Ez2l_9b_XJv53R7Z6vj-3-oR7uk1w55r1iH1bCZq_RmpZEa0ociCUel5la458Ebzg8tCuU" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1126" data-original-width="1513" src="https://blogger.googleusercontent.com/img/a/AVvXsEhIe-77B1wvgfJwbBi7QlsuWYhKJ7enYlT_Yl52RhNcAFJtCvI6bkBdHg9P1i75NLKX0uCDeZvlBlbWWFcThZfCygSgGQd3DwceXYsTjatk9jBTAfWdEhUj8Ez2l_9b_XJv53R7Z6vj-3-oR7uk1w55r1iH1bCZq_RmpZEa0ociCUel5la458Ebzg8tCuU=s16000" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiHLlOwcMTNtOMw7CMSHyt0U1UiTLDipWAr1kCntST_AYafrd2r3QE1lGSZTjfMRQ8fYvd8hZr8MtB9r_REZZWEZMAapqdLIOkq4w4z3fUyNO-NiLnM5H_UJ0vpl91P43rc_2RDcGkEC9JLdMLaFD_0H95AK38g8feZepQ0YfiYov9vbwQUmONMTNd1-44" style="margin-left: 1em; 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<div class="widget-content cloud-label" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; box-sizing: border-box; color: #343434; float: left; font-family: Signika, Arial, sans-serif; font-size: 14px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 290px;"><ul style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; list-style: none; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%201.1%20%3A%20PENGUKURAN%20PANJANG" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 1.1 : PENGUKURAN PANJANG</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%201.2%20%3A%20PENJUMLAHAN%20VEKTOR" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 1.2 : PENJUMLAHAN VEKTOR</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%201.3%20%3A%20GERAK%20LURUS" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 1.3 : GERAK LURUS</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%201.4%20%3A%20HUKUM%20NEWTON%20DAN%20PENERAPANNYA" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 1.4 : HUKUM NEWTON DAN PENERAPANNYA</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%201.5%20%3A%20MOMEN%20GAYA%20MOMEN%20INERSIA%20DAN%20TITIK%20BERAT" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 1.5 : MOMEN GAYA MOMEN INERSIA DAN TITIK BERAT</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%201.6%20%3A%20USAHA%20DAN%20PERUBAHAN%20ENERGI%20MEKANIK" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 1.6 : USAHA DAN PERUBAHAN ENERGI MEKANIK</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%201.7%20%3A%20ELASTISITAS%20DAN%20SUSUSAN%20PEGAS" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 1.7 : ELASTISITAS DAN SUSUSAN PEGAS</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%201.8%20%3A%20HUKUM%20KEKEKALAN%20ENERGI%20MEKANIK" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 1.8 : HUKUM KEKEKALAN ENERGI MEKANIK</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%201.9%20%3A%20MOMENTUM" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 1.9 : MOMENTUM</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%202.1%20%3A%20FLUIDA%20STATIS%20DAN%20FLUIDA%20DINAMIS" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 2.1 : FLUIDA STATIS DAN FLUIDA DINAMIS</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%202.2%20%3A%20KALOR" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 2.2 : KALOR</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%202.3%20%3A%20PERSAMAAN%20GAS%20IDEAL%20DAN%20TERMODINAMIKA" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 2.3 : PERSAMAAN GAS IDEAL DAN TERMODINAMIKA</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%202.4%20%3A%20PROSES%20TERMODINAMIKA%20MESIN%20KALOR" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 2.4 : PROSES TERMODINAMIKA MESIN KALOR</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%202.5%20%3A%20GELOMBANG%20STASIONER" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 2.5 : GELOMBANG STASIONER</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%202.6%20%3A%20GELOMBANG%20ELEKTROMAGNET" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 2.6 : GELOMBANG ELEKTROMAGNET</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%202.7%20%3A%20ALAT%20OPTIK%20MIKROSKOP%20DAN%20TEROPONG" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 2.7 : ALAT OPTIK MIKROSKOP DAN TEROPONG</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%202.8%20%3A%20INTERFERENSI%20DAN%20DIFRAKSI%20CAHAYA" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 2.8 : INTERFERENSI DAN DIFRAKSI CAHAYA</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%202.9%20%3A%20EFEK%20DOPPLER" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 2.9 : EFEK DOPPLER</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.1%20%3A%20INTENSITAS%20DAN%20TARAF%20INTENSITAS" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.1 : INTENSITAS DAN TARAF INTENSITAS</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.2%20%3A%20HUKUM%20COULOMB%20DAN%20MEDAN%20LISTRIK" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.2 : HUKUM COULOMB DAN MEDAN LISTRIK</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.3%20%3A%20POTENSIAL%20LISTRIK%20DAN%20ENERGI%20POTENSIAL%20LISTRIK" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.3 : POTENSIAL LISTRIK DAN ENERGI POTENSIAL LISTRIK</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.4%20%3A%20HUKUM%201%20DAN%202%20KIRCHOFF" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.4 : HUKUM 1 DAN 2 KIRCHOFF</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.5%20%3A%20INDUKSI%20MAGNETIK" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.5 : INDUKSI MAGNETIK</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.6%20%3A%20GAYA%20LORENTZ" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.6 : GAYA LORENTZ</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.7%20%3A%20GAYA%20GERAK%20LISTRIK%20INDUKSI%20DAN%20TRANSFORMATOR" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.7 : GAYA GERAK LISTRIK INDUKSI DAN TRANSFORMATOR</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.8%20%3A%20RANGKAIAN%20RLC%20SERI" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.8 : RANGKAIAN RLC SERI</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.9%20%3A%20TEORI%20ATOM" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.9 : TEORI ATOM</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.1%20%3A%20EFEK%20FOTO%20LISTRIK%20DAN%20EFEK%20COMPTON" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.1 : EFEK FOTO LISTRIK DAN EFEK COMPTON</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.2%20%3A%20TEORI%20RELATIVITAS" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.2 : TEORI RELATIVITAS</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.3%20%3A%20STRUKTUR%20INTI%20ATOM%20DAN%20REAKSI%20INTI" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.3 : STRUKTUR INTI ATOM DAN REAKSI INTI</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.4%20%3A%20MANFAAT%20RADIOISOTOP" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.4 : MANFAAT RADIOISOTOP</a></li></ul></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8185710560472973854.post-78431185452070044882023-11-19T07:41:00.012+07:002023-11-19T07:59:07.956+07:00BAB 4.4 : MANFAAT RADIOISOTOP<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEig5Nzxy229Z7vD-StAiOE8g24fv133WBQvPdHuqKFjyn_LaqqKVYJUx0PJchXsDDqoPsM0XZg1wRBXHt_7ZmEsZuwPJsDvOViFacS4AeK0723G8lKLivHJof0zyWCjRhJNm_GsibwW0FCZG2gzr0oBzaVjAuc8Aiey1UX3vMkJGDN1WLUEhfPArndvqbI" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1214" data-original-width="1532" src="https://blogger.googleusercontent.com/img/a/AVvXsEig5Nzxy229Z7vD-StAiOE8g24fv133WBQvPdHuqKFjyn_LaqqKVYJUx0PJchXsDDqoPsM0XZg1wRBXHt_7ZmEsZuwPJsDvOViFacS4AeK0723G8lKLivHJof0zyWCjRhJNm_GsibwW0FCZG2gzr0oBzaVjAuc8Aiey1UX3vMkJGDN1WLUEhfPArndvqbI=s16000" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><b>BACA JUGA:</b></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="post-body entry-content" id="postBody" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; color: var(--text-font-color); font-family: var(--text-font); font-size: 15px; line-height: 1.8em; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 800px;"><div class="widget-content cloud-label" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; box-sizing: border-box; color: #343434; float: left; font-family: Signika, Arial, sans-serif; font-size: 14px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 290px;"><ul style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; line-height: 1.5em; list-style: none; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.8%20%3A%20RANGKAIAN%20RLC%20SERI" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.8 : RANGKAIAN RLC SERI</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.9%20%3A%20TEORI%20ATOM" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.9 : TEORI ATOM</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.1%20%3A%20EFEK%20FOTO%20LISTRIK%20DAN%20EFEK%20COMPTON" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.1 : EFEK FOTO LISTRIK DAN EFEK COMPTON</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.2%20%3A%20TEORI%20RELATIVITAS" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.2 : TEORI RELATIVITAS</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.3%20%3A%20STRUKTUR%20INTI%20ATOM%20DAN%20REAKSI%20INTI" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.3 : STRUKTUR INTI ATOM DAN REAKSI INTI</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.4%20%3A%20MANFAAT%20RADIOISOTOP" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.4 : MANFAAT RADIOISOTOP</a></li></ul></div></div><div id="ads-holder" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; 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text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEifTSxPs0zodX5PWR6woJYDWMKRh1vKqF3ECvOMcgJeSUbObpsAct6I4nUDgg8bKEd70PzhLBmEkZbctIVxP8wLs-uVq9hOIOOFQ_lxU8HrxhMy51CePgdV5GBHRnP-7n-JyuZvHKj8O8xLjZLZmPC1da6rjO3sW0i2vZBjwZPkZbrTRg1CHLfMo1QOy-0" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="728" data-original-width="1535" src="https://blogger.googleusercontent.com/img/a/AVvXsEifTSxPs0zodX5PWR6woJYDWMKRh1vKqF3ECvOMcgJeSUbObpsAct6I4nUDgg8bKEd70PzhLBmEkZbctIVxP8wLs-uVq9hOIOOFQ_lxU8HrxhMy51CePgdV5GBHRnP-7n-JyuZvHKj8O8xLjZLZmPC1da6rjO3sW0i2vZBjwZPkZbrTRg1CHLfMo1QOy-0=s16000" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><b>BACA JUGA:</b></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="post-body entry-content" id="postBody" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; color: var(--text-font-color); font-family: var(--text-font); font-size: 15px; line-height: 1.8em; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 800px;"><div class="widget-content cloud-label" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; box-sizing: border-box; color: #343434; float: left; font-family: Signika, Arial, sans-serif; font-size: 14px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 290px;"><ul style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; line-height: 1.5em; list-style: none; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.8%20%3A%20RANGKAIAN%20RLC%20SERI" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.8 : RANGKAIAN RLC SERI</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.9%20%3A%20TEORI%20ATOM" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.9 : TEORI ATOM</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.1%20%3A%20EFEK%20FOTO%20LISTRIK%20DAN%20EFEK%20COMPTON" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.1 : EFEK FOTO LISTRIK DAN EFEK COMPTON</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.2%20%3A%20TEORI%20RELATIVITAS" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.2 : TEORI RELATIVITAS</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.3%20%3A%20STRUKTUR%20INTI%20ATOM%20DAN%20REAKSI%20INTI" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.3 : STRUKTUR INTI ATOM DAN REAKSI INTI</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.4%20%3A%20MANFAAT%20RADIOISOTOP" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.4 : MANFAAT RADIOISOTOP</a></li></ul></div></div><div id="ads-holder" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; margin: 15px 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 800px;"></div></div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgQR2n4_IGsGAg5ZMtO_NW2Tv4axVdtH9nzJpssfYd5v4yt5k3YwNlNk5IvaGbsnAJJHW_fvy5U4z9YQn81l16YJd7Cw1BB70gpDaBKNeb_I_gUOj_0y6-wtp8mkVK2X78eB5d2Aibj0brVgnudNHdjrXBOqEGDuNrjVP6Ffu19Jv5KKGe5RiD209Lt_Bc" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="367" data-original-width="1314" src="https://blogger.googleusercontent.com/img/a/AVvXsEgQR2n4_IGsGAg5ZMtO_NW2Tv4axVdtH9nzJpssfYd5v4yt5k3YwNlNk5IvaGbsnAJJHW_fvy5U4z9YQn81l16YJd7Cw1BB70gpDaBKNeb_I_gUOj_0y6-wtp8mkVK2X78eB5d2Aibj0brVgnudNHdjrXBOqEGDuNrjVP6Ffu19Jv5KKGe5RiD209Lt_Bc=s16000" /></a></div><div class="separator" style="clear: both; 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text-align: center;"><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><b>BACA JUGA:</b></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="post-body entry-content" id="postBody" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; color: var(--text-font-color); font-family: var(--text-font); font-size: 15px; line-height: 1.8em; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 800px;"><div class="widget-content cloud-label" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; box-sizing: border-box; color: #343434; float: left; font-family: Signika, Arial, sans-serif; font-size: 14px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 290px;"><ul style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; line-height: 1.5em; list-style: none; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.8%20%3A%20RANGKAIAN%20RLC%20SERI" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.8 : RANGKAIAN RLC SERI</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.9%20%3A%20TEORI%20ATOM" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.9 : TEORI ATOM</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.1%20%3A%20EFEK%20FOTO%20LISTRIK%20DAN%20EFEK%20COMPTON" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.1 : EFEK FOTO LISTRIK DAN EFEK COMPTON</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.2%20%3A%20TEORI%20RELATIVITAS" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.2 : TEORI RELATIVITAS</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.3%20%3A%20STRUKTUR%20INTI%20ATOM%20DAN%20REAKSI%20INTI" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.3 : STRUKTUR INTI ATOM DAN REAKSI INTI</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.4%20%3A%20MANFAAT%20RADIOISOTOP" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.4 : MANFAAT RADIOISOTOP</a></li></ul></div></div><div id="ads-holder" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; margin: 15px 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 800px;"></div></div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiRLdQ3_iWy6Tpb-eLEjirlUyUZ9dMLO1jqTCDJXj4WT3CY1GJM3WsRhlEk7Sa-l1bIUDq2MCeEGovYlbrKzarh7yWDgB7jsB5doaKi2Lrl3GKLuvJLYxjDKmGtDeNIDkh2XD7srXKUrd-4C3XUfbvJ3w-_laXO34yDaYkwTpQ00LvEn9dumC-N6j92RaY" style="margin-left: 1em; 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text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiNHHL2qiYxTlniMaNrxhEuAQ49xProjMsPRCqlTdvEyoLjrmjHb7oZbHiyjr83MtoV6VuVDnX5Ix8lGJiXQgYo6q9T30oJFjVgA4giCtoOY1nS8LlUOD19kFAkbKoLOzoXFzGI9DjNYg1RzUfE4i_2SSpOP83v3eua3oBqUpQoZO8WDoTTaD5uCV0cS-8" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1761" data-original-width="1534" src="https://blogger.googleusercontent.com/img/a/AVvXsEiNHHL2qiYxTlniMaNrxhEuAQ49xProjMsPRCqlTdvEyoLjrmjHb7oZbHiyjr83MtoV6VuVDnX5Ix8lGJiXQgYo6q9T30oJFjVgA4giCtoOY1nS8LlUOD19kFAkbKoLOzoXFzGI9DjNYg1RzUfE4i_2SSpOP83v3eua3oBqUpQoZO8WDoTTaD5uCV0cS-8=s16000" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><b>BACA JUGA:</b></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="post-body entry-content" id="postBody" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; color: var(--text-font-color); font-family: var(--text-font); font-size: 15px; line-height: 1.8em; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 800px;"><div class="widget-content cloud-label" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; box-sizing: border-box; color: #343434; float: left; font-family: Signika, Arial, sans-serif; font-size: 14px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 290px;"><ul style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; line-height: 1.5em; list-style: none; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.8%20%3A%20RANGKAIAN%20RLC%20SERI" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.8 : RANGKAIAN RLC SERI</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.9%20%3A%20TEORI%20ATOM" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.9 : TEORI ATOM</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.1%20%3A%20EFEK%20FOTO%20LISTRIK%20DAN%20EFEK%20COMPTON" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.1 : EFEK FOTO LISTRIK DAN EFEK COMPTON</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.2%20%3A%20TEORI%20RELATIVITAS" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.2 : TEORI RELATIVITAS</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.3%20%3A%20STRUKTUR%20INTI%20ATOM%20DAN%20REAKSI%20INTI" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.3 : STRUKTUR INTI ATOM DAN REAKSI INTI</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.4%20%3A%20MANFAAT%20RADIOISOTOP" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.4 : MANFAAT RADIOISOTOP</a></li></ul></div></div><div id="ads-holder" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; margin: 15px 0px; outline: 0px; overflow: hidden; padding: 0px; vertical-align: baseline; width: 800px;"></div></div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj0Zr3KVAnki5OIDAFwOyR3v146xoMW1RVPlhFsSaGP9kjFUycTPwmOIJ9tJX8skkpR1Fh4NmVlhBbNizTl3_XdkhoYQeQ8OKFxTdyz1J0Ee5aGLyzUhVBWNVWDVbeTWUPZGwsXjE0_jA7ZtSe9OOQsxdMdQNPwi1cwtSFX3eV4fTzKPb3XO6xwf65fhK0" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="339" data-original-width="1311" src="https://blogger.googleusercontent.com/img/a/AVvXsEj0Zr3KVAnki5OIDAFwOyR3v146xoMW1RVPlhFsSaGP9kjFUycTPwmOIJ9tJX8skkpR1Fh4NmVlhBbNizTl3_XdkhoYQeQ8OKFxTdyz1J0Ee5aGLyzUhVBWNVWDVbeTWUPZGwsXjE0_jA7ZtSe9OOQsxdMdQNPwi1cwtSFX3eV4fTzKPb3XO6xwf65fhK0=s16000" /></a></div><div class="separator" style="clear: both; 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text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgr_GWbfawmR4Ob8RAsewhUImQ9_7_fd4eM3xjHYLmnWdW7_DAYDYlUIQ_RGTEgTvtDzm5uOdLQoC_bDbz9JexivELAW1cg2BpC68nxs-itUPwhDgsCC1dimZSUprlqAsbB11kHzddl5hcZGkEx5VeDzrJpQajP7cUWZjdFrW9rM_G9us5D8ju34FgpBJ0" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1706" data-original-width="1532" src="https://blogger.googleusercontent.com/img/a/AVvXsEgr_GWbfawmR4Ob8RAsewhUImQ9_7_fd4eM3xjHYLmnWdW7_DAYDYlUIQ_RGTEgTvtDzm5uOdLQoC_bDbz9JexivELAW1cg2BpC68nxs-itUPwhDgsCC1dimZSUprlqAsbB11kHzddl5hcZGkEx5VeDzrJpQajP7cUWZjdFrW9rM_G9us5D8ju34FgpBJ0=s16000" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEimEspGAfGVa5a_kAdDnRG-kopfWm66RHeePdj7EiaOzZ3U0Lav_3ZY7pGwphanf7H_IN_zIDciSt3Tm81uUKRVU5g0pF0p9JKMjSLc8m_jC0ZKoR8QcgaAK8Zm48y328UakiyiCBa0da479gqgy3AY3pm_-WosqTrkt3WUQjrJP8CCUTknvblFmJoAsJc" style="margin-left: 1em; 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margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 800px;"><div class="widget-content cloud-label" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; box-sizing: border-box; color: #343434; float: left; font-family: Signika, Arial, sans-serif; font-size: 14px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 290px;"><ul style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; line-height: 1.5em; list-style: none; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.8%20%3A%20RANGKAIAN%20RLC%20SERI" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.8 : RANGKAIAN RLC SERI</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.9%20%3A%20TEORI%20ATOM" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.9 : TEORI ATOM</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.1%20%3A%20EFEK%20FOTO%20LISTRIK%20DAN%20EFEK%20COMPTON" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.1 : EFEK FOTO LISTRIK DAN EFEK COMPTON</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.2%20%3A%20TEORI%20RELATIVITAS" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.2 : TEORI RELATIVITAS</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.3%20%3A%20STRUKTUR%20INTI%20ATOM%20DAN%20REAKSI%20INTI" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.3 : STRUKTUR INTI ATOM DAN REAKSI INTI</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.4%20%3A%20MANFAAT%20RADIOISOTOP" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.4 : MANFAAT RADIOISOTOP</a></li></ul></div></div><div id="ads-holder" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; 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text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiHqXriGHdJD-yiTEruMfUEWWt5aJBqJl8ib72KZBLJ8J2tsXBC2HmB-1p6lc6p4d6MhkYaB0i2ad6zCPxsyqhR01Yex7jDlwmOmASPsLhgg2sY_4Gouu7P0eJIvK2VAbE-V5RMlQzmOcZl_OyZSlH8aZwAMm06a6AhN6sl29GJKnKw7vmmDHIsfqOifdE" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1680" data-original-width="1536" src="https://blogger.googleusercontent.com/img/a/AVvXsEiHqXriGHdJD-yiTEruMfUEWWt5aJBqJl8ib72KZBLJ8J2tsXBC2HmB-1p6lc6p4d6MhkYaB0i2ad6zCPxsyqhR01Yex7jDlwmOmASPsLhgg2sY_4Gouu7P0eJIvK2VAbE-V5RMlQzmOcZl_OyZSlH8aZwAMm06a6AhN6sl29GJKnKw7vmmDHIsfqOifdE=s16000" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjyArQuQiLfgfP5oXadSr47MVb3lp67A2REZ3dvUYKOJ8YI4QbH-K_93mDKz25HaaycF70-8077ECM2mrc4jsmrJRcD3cO7_sCyj2Xvz1RH3UM0H-Xc5V7nuvhZhe67nGLGQY8WP8VFxfpIjVuSHmE6q1rBkYLVj4uGOGQqm8ze2MJwzZTpcXAAkGlS-lA" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1974" data-original-width="1531" src="https://blogger.googleusercontent.com/img/a/AVvXsEjyArQuQiLfgfP5oXadSr47MVb3lp67A2REZ3dvUYKOJ8YI4QbH-K_93mDKz25HaaycF70-8077ECM2mrc4jsmrJRcD3cO7_sCyj2Xvz1RH3UM0H-Xc5V7nuvhZhe67nGLGQY8WP8VFxfpIjVuSHmE6q1rBkYLVj4uGOGQqm8ze2MJwzZTpcXAAkGlS-lA=s16000" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><b>BACA JUGA:</b></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="post-body entry-content" id="postBody" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; color: var(--text-font-color); font-family: var(--text-font); font-size: 15px; line-height: 1.8em; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 800px;"><div class="widget-content cloud-label" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; box-sizing: border-box; color: #343434; float: left; font-family: Signika, Arial, sans-serif; font-size: 14px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline; width: 290px;"><ul style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; line-height: 1.5em; list-style: none; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.8%20%3A%20RANGKAIAN%20RLC%20SERI" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.8 : RANGKAIAN RLC SERI</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%203.9%20%3A%20TEORI%20ATOM" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 3.9 : TEORI ATOM</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.1%20%3A%20EFEK%20FOTO%20LISTRIK%20DAN%20EFEK%20COMPTON" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.1 : EFEK FOTO LISTRIK DAN EFEK COMPTON</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.2%20%3A%20TEORI%20RELATIVITAS" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.2 : TEORI RELATIVITAS</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.3%20%3A%20STRUKTUR%20INTI%20ATOM%20DAN%20REAKSI%20INTI" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.3 : STRUKTUR INTI ATOM DAN REAKSI INTI</a></li><li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border: 0px; float: left; line-height: 1.2; list-style: none; margin: 0px 5px 5px 0px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><a class="label-name" href="https://prima.fisikasiswa.com/search/label/BAB%204.4%20%3A%20MANFAAT%20RADIOISOTOP" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; border-radius: 4px; border: 1px solid var(--cloud-border-color); display: block; height: 26px; line-height: 26px; margin: 0px; outline: 0px; overflow: hidden; padding: 0px 10px; text-decoration-line: none; transition: all 0.3s ease 0s; vertical-align: baseline;">BAB 4.4 : MANFAAT RADIOISOTOP</a></li></ul></div></div><div id="ads-holder" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px 50%; background-repeat: initial; background-size: initial; 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text-align: center;"><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><h3 style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px center; background-repeat: initial; background-size: initial; border: 0px; color: var(--theme-text-color); font-family: Signika, Arial, sans-serif; line-height: 1.5em; margin: 0px 0px 15px; outline: 0px; padding: 0px; position: relative; text-align: center; vertical-align: baseline;"><div style="text-align: left;"><span style="color: var(--theme-text-color);">BACA JUGA:</span></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-33-potensial-listrik-dan-energi.html" target="_blank"><span style="font-size: small;">BAB 3.3 : POTENSIAL LISTRIK DAN ENERGI POTENSIAL LISTRIK</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-34-hukum-1-dan-2-kirchoff.html" target="_blank"><span style="font-size: small;">BAB 3.4 : HUKUM 1 DAN 2 KIRCHOFF</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-35-induksi-magnetik.html" target="_blank"><span style="font-size: small;">BAB 3.5 : INDUKSI MAGNETIK</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-36-gaya-lorentz.html" target="_blank"><span style="font-size: small;">BAB 3.6 : GAYA LORENTZ</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-37-gaya-gerak-listrik-induksi-dan.html" target="_blank"></a><a href="https://prima.fisikasiswa.com/2023/11/bab-37-gaya-gerak-listrik-induksi-dan.html" target="_blank"><span style="font-size: small;">BAB 3.7 : GAYA GERAK LISTRIK INDUKSI DAN TRANSFORMATOR</span></a></div></h3></div><div class="separator" style="clear: both; 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text-align: center;"><br /></div></div></div></div></div></div></div></div></div></div></div></div></div><p></p>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8185710560472973854.post-67085002004029064452023-11-18T21:16:00.014+07:002023-11-19T06:56:49.090+07:00BAB 3.6 : GAYA LORENTZ<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiPpV__O_bth-q1nzbeArz-AJcJBHxBkjMqY3OxXxH4-0ntI_rANKHHjGe2nhHarjQl43vDM6OJhr9VrV2fhYRvPotg80GRTJE8TnMFgLdpDR914UtZytTMPKnHv0ceUNX-gDCuuyjLqg2kb_bUAPMKPO3b_2cshwk6fis6Zm2Aog_hl2WQ9K3w4IxKFiU" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1680" data-original-width="1531" src="https://blogger.googleusercontent.com/img/a/AVvXsEiPpV__O_bth-q1nzbeArz-AJcJBHxBkjMqY3OxXxH4-0ntI_rANKHHjGe2nhHarjQl43vDM6OJhr9VrV2fhYRvPotg80GRTJE8TnMFgLdpDR914UtZytTMPKnHv0ceUNX-gDCuuyjLqg2kb_bUAPMKPO3b_2cshwk6fis6Zm2Aog_hl2WQ9K3w4IxKFiU=s16000" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><h3 style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px center; background-repeat: initial; background-size: initial; border: 0px; color: var(--theme-text-color); font-family: Signika, Arial, sans-serif; line-height: 1.5em; margin: 0px 0px 15px; outline: 0px; padding: 0px; position: relative; text-align: center; vertical-align: baseline;"><div style="text-align: left;"><span style="color: var(--theme-text-color);">BACA JUGA:</span></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-33-potensial-listrik-dan-energi.html" target="_blank"><span style="font-size: small;">BAB 3.3 : POTENSIAL LISTRIK DAN ENERGI POTENSIAL LISTRIK</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-34-hukum-1-dan-2-kirchoff.html" target="_blank"><span style="font-size: small;">BAB 3.4 : HUKUM 1 DAN 2 KIRCHOFF</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-35-induksi-magnetik.html" target="_blank"><span style="font-size: small;">BAB 3.5 : INDUKSI MAGNETIK</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-36-gaya-lorentz.html" target="_blank"><span style="font-size: small;">BAB 3.6 : GAYA LORENTZ</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-37-gaya-gerak-listrik-induksi-dan.html" target="_blank"></a><a href="https://prima.fisikasiswa.com/2023/11/bab-37-gaya-gerak-listrik-induksi-dan.html" target="_blank"><span style="font-size: small;">BAB 3.7 : GAYA GERAK LISTRIK INDUKSI DAN TRANSFORMATOR</span></a></div></h3></div><div class="separator" style="clear: both; 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text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjUqUCOtiP_XNL3lyq4FyQ00yWMW6aK0EoFfvdAmSd1y0sJoUwCdCPI-Mg0_dQklmJNu8uekX0zfHyQfWGWShATJO6id0kxxPxriXe1OeY2Mk56ciO1eaNjSpfSCWLdvjhUE_Lacqy_RG9vEDKu628-ZDTHOVJQPjOPkBVjzO9lahc1DoLFtMadIOqlGy0" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1785" data-original-width="1539" src="https://blogger.googleusercontent.com/img/a/AVvXsEjUqUCOtiP_XNL3lyq4FyQ00yWMW6aK0EoFfvdAmSd1y0sJoUwCdCPI-Mg0_dQklmJNu8uekX0zfHyQfWGWShATJO6id0kxxPxriXe1OeY2Mk56ciO1eaNjSpfSCWLdvjhUE_Lacqy_RG9vEDKu628-ZDTHOVJQPjOPkBVjzO9lahc1DoLFtMadIOqlGy0=s16000" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><h3 style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px center; background-repeat: initial; background-size: initial; border: 0px; color: var(--theme-text-color); font-family: Signika, Arial, sans-serif; line-height: 1.5em; margin: 0px 0px 15px; outline: 0px; padding: 0px; position: relative; text-align: center; vertical-align: baseline;"><div style="text-align: left;"><span style="color: var(--theme-text-color);">BACA JUGA:</span></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-33-potensial-listrik-dan-energi.html" target="_blank"><span style="font-size: small;">BAB 3.3 : POTENSIAL LISTRIK DAN ENERGI POTENSIAL LISTRIK</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-34-hukum-1-dan-2-kirchoff.html" target="_blank"><span style="font-size: small;">BAB 3.4 : HUKUM 1 DAN 2 KIRCHOFF</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-35-induksi-magnetik.html" target="_blank"><span style="font-size: small;">BAB 3.5 : INDUKSI MAGNETIK</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-36-gaya-lorentz.html" target="_blank"><span style="font-size: small;">BAB 3.6 : GAYA LORENTZ</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-37-gaya-gerak-listrik-induksi-dan.html" target="_blank"></a><a href="https://prima.fisikasiswa.com/2023/11/bab-37-gaya-gerak-listrik-induksi-dan.html" target="_blank"><span style="font-size: small;">BAB 3.7 : GAYA GERAK LISTRIK INDUKSI DAN TRANSFORMATOR</span></a></div></h3></div><div class="separator" style="clear: both; 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margin-right: 1em;"><img alt="" data-original-height="2015" data-original-width="1535" src="https://blogger.googleusercontent.com/img/a/AVvXsEhSCD39ohZ1mRPq3r0rvIkkDEitDt83XlW5r6R8DIHGTli67aO1Mvb4Oh5TyrZA7GAwWF6-OktiaiGbyrKkuP9zjNmlLRbjW663bpn_zXQWUGN_z9DsH_JXoWoZxyknCi4cEq_6-pYYvi1Ls8Kw4_gEkeqpjsQGquen9j1SOBZRwLDoDN_j5Zxul4iSEFU=s16000" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><h3 style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px center; background-repeat: initial; background-size: initial; border: 0px; color: var(--theme-text-color); font-family: Signika, Arial, sans-serif; line-height: 1.5em; margin: 0px 0px 15px; outline: 0px; padding: 0px; position: relative; text-align: center; vertical-align: baseline;"><div style="text-align: left;"><span style="color: var(--theme-text-color);">BACA JUGA:</span></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-33-potensial-listrik-dan-energi.html" target="_blank"><span style="font-size: small;">BAB 3.3 : POTENSIAL LISTRIK DAN ENERGI POTENSIAL LISTRIK</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-34-hukum-1-dan-2-kirchoff.html" target="_blank"><span style="font-size: small;">BAB 3.4 : HUKUM 1 DAN 2 KIRCHOFF</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-35-induksi-magnetik.html" target="_blank"><span style="font-size: small;">BAB 3.5 : INDUKSI MAGNETIK</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-36-gaya-lorentz.html" target="_blank"><span style="font-size: small;">BAB 3.6 : GAYA LORENTZ</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-37-gaya-gerak-listrik-induksi-dan.html" target="_blank"></a><a href="https://prima.fisikasiswa.com/2023/11/bab-37-gaya-gerak-listrik-induksi-dan.html" target="_blank"><span style="font-size: small;">BAB 3.7 : GAYA GERAK LISTRIK INDUKSI DAN TRANSFORMATOR</span></a></div></h3></div><div class="separator" style="clear: both; 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text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEi0MWX3fnuZZe9RilDG41ACqpAfg3U8tQ_AFJYkUQgJ0puUTAI7jZ0x_4MeHvQo77zOwjG_8ihINjcgAJ8r4dcGKx3UYzQ9IaxBf1wAJ_ypRmlMNNX05vTLX6kQl_ZeRN4bbiN3zF2Jol8SRwLN5kGr0IRgoqGQg6ylyrS5JIwuF5CtFKPNrGLPGIxlew4" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1657" data-original-width="1532" src="https://blogger.googleusercontent.com/img/a/AVvXsEi0MWX3fnuZZe9RilDG41ACqpAfg3U8tQ_AFJYkUQgJ0puUTAI7jZ0x_4MeHvQo77zOwjG_8ihINjcgAJ8r4dcGKx3UYzQ9IaxBf1wAJ_ypRmlMNNX05vTLX6kQl_ZeRN4bbiN3zF2Jol8SRwLN5kGr0IRgoqGQg6ylyrS5JIwuF5CtFKPNrGLPGIxlew4=s16000" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgwDTyNG0wHMtLv1upMFEIVnB8DhZJKiKvm0cfldXMlPKE58D5o6vz53oMcSzAlTL8wOgwKgkU9YnhsTCfD7ZS9ut8OYWj216adCo_WlR2PUUTa1Taka_yoLDAfFi8Likc9JmOBxxZbaAJm9knojYhot8SHjjKhxnsmIkOqcHgWl0SzhYq8GU_Yd4JVSyk" style="margin-left: 1em; 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text-align: center;"><h3 style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: 0px center; background-repeat: initial; background-size: initial; border: 0px; color: var(--theme-text-color); font-family: Signika, Arial, sans-serif; line-height: 1.5em; margin: 0px 0px 15px; outline: 0px; padding: 0px; position: relative; vertical-align: baseline;"><div style="text-align: left;"><span style="color: var(--theme-text-color);"><br /></span></div><div style="text-align: left;"><span style="color: var(--theme-text-color);">BACA JUGA:</span></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-33-potensial-listrik-dan-energi.html" target="_blank"><span style="font-size: small;">BAB 3.3 : POTENSIAL LISTRIK DAN ENERGI POTENSIAL LISTRIK</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-34-hukum-1-dan-2-kirchoff.html" target="_blank"><span style="font-size: small;">BAB 3.4 : HUKUM 1 DAN 2 KIRCHOFF</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-35-induksi-magnetik.html" target="_blank"><span style="font-size: small;">BAB 3.5 : INDUKSI MAGNETIK</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-36-gaya-lorentz.html" target="_blank"><span style="font-size: small;">BAB 3.6 : GAYA LORENTZ</span></a></div><div style="text-align: left;"><a href="https://prima.fisikasiswa.com/2023/11/bab-37-gaya-gerak-listrik-induksi-dan.html" target="_blank"></a><a href="https://prima.fisikasiswa.com/2023/11/bab-37-gaya-gerak-listrik-induksi-dan.html" target="_blank"><span style="font-size: small;">BAB 3.7 : GAYA GERAK LISTRIK INDUKSI DAN TRANSFORMATOR</span></a></div></h3><div class="separator" style="clear: both; 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margin-right: 1em;"><img alt="" data-original-height="524" data-original-width="1320" src="https://blogger.googleusercontent.com/img/a/AVvXsEiXpT58D6JGVqn6tmDsU5iM0NwAqDXEK7vhCfTghF-2-ifaIb7pd_iKGrBP7bs2Cn_V9W9RpwwvGys6KQlhQDisZnCG-k_9IaWX1Ggl1V3dxSLHbOta54-JopwocjVevgDB264eLgKoYxLjnJuZlLDtqfXu8Cjzh-YexYO3DPqGO30ElCT-N-BDE0ffprc=s16000" /></a></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div><p></p>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8185710560472973854.post-25798266197179659562023-11-18T19:08:00.011+07:002023-11-19T06:41:50.230+07:00BAB 3.2 : HUKUM COULOMB DAN MEDAN LISTRIK<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgJz7vXj7utW8eyXARbAx4LR0kkxffD5SKoZUUK2SC_ZCDvWSl0x1q9i501XpLs3-oG_drm9kuTemFrfNGLVXfnQgQ3hs77Hvj_0XNV1d5F-aVqJ2V32Z2zOSsrgtwPrHkQ1jZCtQz8lLvfRp1Hj4JoBMuntKkjulVREsTTerwN9RzFhRRF8rkCLPZNnAk" style="margin-left: 1em; 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text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg-e32yJmtC0cgdLOMcPrdeGbV012wzhkeNu4tX-nQP9vB0YeGNLy3W_yekt5ehjoFan4oMLaaFoDtF4OqiGzKEEZK5Y7LX5VrzoJu2e9Li1b820YwlfPqkHFW-FhkNTnRych8YRuNgkaMYaUnF7jaAp2YCIlNfTaFzglw9y-6kQfAozaibOq0DNgnFvug" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="2010" data-original-width="1534" src="https://blogger.googleusercontent.com/img/a/AVvXsEg-e32yJmtC0cgdLOMcPrdeGbV012wzhkeNu4tX-nQP9vB0YeGNLy3W_yekt5ehjoFan4oMLaaFoDtF4OqiGzKEEZK5Y7LX5VrzoJu2e9Li1b820YwlfPqkHFW-FhkNTnRych8YRuNgkaMYaUnF7jaAp2YCIlNfTaFzglw9y-6kQfAozaibOq0DNgnFvug=s16000" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: left;"><table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;">
<tbody><tr>
<td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 467.5pt;" valign="top" width="779">
<p class="MsoNormal" style="line-height: 18.0pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><b><span style="font-family: Arial, "sans-serif"; font-size: 12pt;">BACA JUGA:</span></b><b><span style="font-family: Arial, "sans-serif"; font-size: 13.5pt;"><o:p></o:p></span></b></p>
<p class="MsoNormal" style="line-height: 18.0pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><b><span style="font-family: Arial, "sans-serif"; font-size: 13.5pt;"><a href="https://www.blogger.com/u/2/blog/post/edit/8185710560472973854/23658299933593817"><span style="color: blue; font-size: 12.0pt;">BAB 2.7 : ALAT OPTIK MIKROSKOP DAN
TEROPONG</span></a><o:p></o:p></span></b></p>
<p class="MsoNormal" style="line-height: 18.0pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><b><span style="font-family: Arial, "sans-serif"; font-size: 13.5pt;"><a href="https://www.blogger.com/u/2/blog/post/edit/8185710560472973854/23658299933593817"><span style="color: blue; font-size: 12.0pt;">BAB 2.8 : INTERFERENSI DAN DIFRAKSI
CAHAYA</span></a><o:p></o:p></span></b></p>
<p class="MsoNormal" style="line-height: 18.0pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><b><span style="font-family: Arial, "sans-serif"; font-size: 13.5pt;"><a href="https://www.blogger.com/u/2/blog/post/edit/8185710560472973854/23658299933593817"><span style="color: blue; font-size: 12.0pt;">BAB 2.9 : EFEK DOPPLER</span></a><o:p></o:p></span></b></p>
<p class="MsoNormal" style="line-height: 18.0pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><b><span style="font-family: Arial, "sans-serif"; font-size: 13.5pt;"><a href="https://www.blogger.com/u/2/blog/post/edit/8185710560472973854/23658299933593817"><span style="color: blue; font-size: 12.0pt;">BAB 3.1 : INTENSITAS DAN TARAF INTENSITAS</span></a><o:p></o:p></span></b></p>
<p class="MsoNormal" style="line-height: 18.0pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><b><span style="font-family: Arial, "sans-serif"; font-size: 13.5pt;"><a href="https://www.blogger.com/u/2/blog/post/edit/8185710560472973854/23658299933593817"><span style="color: blue; font-size: 12.0pt;">BAB 3.2 : HUKUM COULOMB DAN MEDAN LISTRIK</span></a><o:p></o:p></span></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><o:p> </o:p></p>
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mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;"><tbody><tr><td style="border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 467.5pt;" valign="top" width="779"><p class="MsoNormal" style="line-height: 18pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><b><span face="Arial, "sans-serif"" style="font-size: 12pt;">BACA JUGA:</span></b><b><span face="Arial, "sans-serif"" style="font-size: 13.5pt;"><o:p></o:p></span></b></p><p class="MsoNormal" style="line-height: 18pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><b><span face="Arial, "sans-serif"" style="font-size: 13.5pt;"><span style="color: blue; font-size: 12pt;"><a href="https://prima.fisikasiswa.com/2023/11/bab-27-alat-optik-mikroskop-dan-teropong.html" target="_blank">BAB 2.7 : ALAT OPTIK MIKROSKOP DAN TEROPONG</a></span><o:p></o:p></span></b></p><p class="MsoNormal" style="line-height: 18pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><b><span face="Arial, "sans-serif"" style="font-size: 13.5pt;"><span style="color: blue; font-size: 12pt;"><a href="https://prima.fisikasiswa.com/2023/11/bab-28-interferensi-dan-difraksi-cahaya.html" target="_blank">BAB 2.8 : INTERFERENSI DAN DIFRAKSI CAHAYA</a></span><o:p></o:p></span></b></p><p class="MsoNormal" style="line-height: 18pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><b><span face="Arial, "sans-serif"" style="font-size: 13.5pt;"><span style="color: blue; font-size: 12pt;"><a href="https://prima.fisikasiswa.com/2023/11/bab-29-efek-doppler.html" target="_blank">BAB 2.9 : EFEK DOPPLER</a></span><o:p></o:p></span></b></p><p class="MsoNormal" style="line-height: 18pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><b><span face="Arial, "sans-serif"" style="font-size: 13.5pt;"><span style="color: blue; font-size: 12pt;"><a href="https://prima.fisikasiswa.com/2023/11/bab-31-intensitas-dan-taraf-intensitas.html" target="_blank">BAB 3.1 : INTENSITAS DAN TARAF INTENSITAS</a></span><o:p></o:p></span></b></p><p class="MsoNormal" style="line-height: 18pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><a href="https://prima.fisikasiswa.com/2023/11/bab-32-hukum-coulomb-dan-medan-listrik.html" target="_blank"><b><span face="Arial, "sans-serif"" style="font-size: 13.5pt;"><span style="color: blue; font-size: 12pt;">BAB 3.2 : HUKUM COULOMB DAN MEDAN LISTRIK</span></span></b> </a></p></td></tr></tbody></table></h3></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhd2eiWUcCES5Vj_SSOREyEB2UJeJcHKsxDZxi9cLBOvJVZbJq49chf5mqDH9jf_7MXeiMIKM6C8MJnDFwwV2J3Pv5PUS-7vvdU5Kp4AmAXxSXMTBX9sDDvRRnpENxpjhYdiKWOG8Vq-2x-IPzYYH3KHZ-g35DinCOimZE0liLU0gtcagsuqUS34MG_ASo" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="515" data-original-width="1313" src="https://blogger.googleusercontent.com/img/a/AVvXsEhd2eiWUcCES5Vj_SSOREyEB2UJeJcHKsxDZxi9cLBOvJVZbJq49chf5mqDH9jf_7MXeiMIKM6C8MJnDFwwV2J3Pv5PUS-7vvdU5Kp4AmAXxSXMTBX9sDDvRRnpENxpjhYdiKWOG8Vq-2x-IPzYYH3KHZ-g35DinCOimZE0liLU0gtcagsuqUS34MG_ASo=s16000" /></a></div><div class="separator" style="clear: both; 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text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhqM9JizqNFwMzMi_YJ56uQ9oZU_ybndVnp2rtO59EoDqeBWDCILWDmsV1sDgTOe0P8zmfidh7ZuiY1Uh96tl_3uQK8gVByK_Jl9L3y2w574s9apqCt2deqnROY_lueBZRwTJ5-okr_KVAkPgfJWeauDmY4oOk7pRHz9BfJV4etLeeC-r_lEiJjeN5gdKA" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1747" data-original-width="1531" src="https://blogger.googleusercontent.com/img/a/AVvXsEhqM9JizqNFwMzMi_YJ56uQ9oZU_ybndVnp2rtO59EoDqeBWDCILWDmsV1sDgTOe0P8zmfidh7ZuiY1Uh96tl_3uQK8gVByK_Jl9L3y2w574s9apqCt2deqnROY_lueBZRwTJ5-okr_KVAkPgfJWeauDmY4oOk7pRHz9BfJV4etLeeC-r_lEiJjeN5gdKA=s16000" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgzoeh6C4iniOsB5Rdpe6HuDs3XHX7_sHU4DbxaMIchqMed43mQSdid53BrXZdq0PdZgjUB36061Xi5_BbsFdUquvzcQLRjwy7WWITt70N0Mj2g7SVIT7mm_6nq1oVs9W0YzS8GcH_-0Er7pXEsJyngmG66J70-WXTdU89K983Q9mLHOAD6PRHLCxE970g" style="margin-left: 1em; 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border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;"><tbody><tr><td style="border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 467.5pt;" valign="top" width="779"><p class="MsoNormal" style="line-height: 18pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><b><span face="Arial, "sans-serif"" style="font-size: 12pt;">BACA JUGA:</span></b><b><span face="Arial, "sans-serif"" style="font-size: 13.5pt;"><o:p></o:p></span></b></p><p class="MsoNormal" style="line-height: 18pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><b><span face="Arial, "sans-serif"" style="font-size: 13.5pt;"><span style="color: blue; font-size: 12pt;"><a href="https://prima.fisikasiswa.com/2023/11/bab-27-alat-optik-mikroskop-dan-teropong.html" target="_blank">BAB 2.7 : ALAT OPTIK MIKROSKOP DAN TEROPONG</a></span><o:p></o:p></span></b></p><p class="MsoNormal" style="line-height: 18pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><b><span face="Arial, "sans-serif"" style="font-size: 13.5pt;"><span style="color: blue; font-size: 12pt;"><a href="https://prima.fisikasiswa.com/2023/11/bab-28-interferensi-dan-difraksi-cahaya.html" target="_blank">BAB 2.8 : INTERFERENSI DAN DIFRAKSI CAHAYA</a></span><o:p></o:p></span></b></p><p class="MsoNormal" style="line-height: 18pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><b><span face="Arial, "sans-serif"" style="font-size: 13.5pt;"><span style="color: blue; font-size: 12pt;"><a href="https://prima.fisikasiswa.com/2023/11/bab-29-efek-doppler.html" target="_blank">BAB 2.9 : EFEK DOPPLER</a></span><o:p></o:p></span></b></p><p class="MsoNormal" style="line-height: 18pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><b><span face="Arial, "sans-serif"" style="font-size: 13.5pt;"><span style="color: blue; font-size: 12pt;"><a href="https://prima.fisikasiswa.com/2023/11/bab-31-intensitas-dan-taraf-intensitas.html" target="_blank">BAB 3.1 : INTENSITAS DAN TARAF INTENSITAS</a></span><o:p></o:p></span></b></p><p class="MsoNormal" style="line-height: 18pt; margin-bottom: 11.25pt; mso-outline-level: 3; vertical-align: baseline;"><a href="https://prima.fisikasiswa.com/2023/11/bab-32-hukum-coulomb-dan-medan-listrik.html" target="_blank"><b><span face="Arial, "sans-serif"" style="font-size: 13.5pt;"><span style="color: blue; font-size: 12pt;">BAB 3.2 : HUKUM COULOMB DAN MEDAN LISTRIK</span></span></b> </a></p></td></tr></tbody></table></h3></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgxJzp6AARtbl0orfr8ffFBtvO0V8Pgj_ySQX7t_QQnmsWfuZgLLCfI6SQTF_sFZzvZGp_QNulPUwNXMIPtlJGAuH-r-3n706GDBNYy7utj383cX0FQ7sVvswcMsviBiJ8NMHZJ3wv4rh8v8wMMjLAf4xJsu_Jg-whC3ivFkawXf-oXw0buqeH_z7eFUAM" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="475" data-original-width="1313" src="https://blogger.googleusercontent.com/img/a/AVvXsEgxJzp6AARtbl0orfr8ffFBtvO0V8Pgj_ySQX7t_QQnmsWfuZgLLCfI6SQTF_sFZzvZGp_QNulPUwNXMIPtlJGAuH-r-3n706GDBNYy7utj383cX0FQ7sVvswcMsviBiJ8NMHZJ3wv4rh8v8wMMjLAf4xJsu_Jg-whC3ivFkawXf-oXw0buqeH_z7eFUAM=s16000" /></a></div><div class="separator" style="clear: both; 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