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In the same way as the logarithm reverses [[exponentiation]], the [[complex logarithm]] is the [[inverse function]] of the exponential function, whether applied to [[real number]]s or [[complex number]]s. The modular [[discrete logarithm]] is another variant; it has uses in [[public-key cryptography]].
==MotivationMotivasi==
[[FileBerkas: Binary logarithm plot with grid.png|right|thumb|upright=1.35|alt=GraphGrafik showingyang amenunjukkan logarithmickurva curvelogaritmik, crossingmelintasi thesumbu ''x''-axis atdiantara ''x''= 1 anddan approachingmendekati minus infinitytak-hingga along thesepanjang sumbu-''y''-axis.|The [[graphfungsi of a functiongraf|graphgrafik]] ofdari thebasis logarithm baselogaritma 2 crosses thememotong [[sumbu x axis|sumbu-''x''-axis]] atantara {{math|''x'' {{=}} 1}} and passes throughdan themelewati pointstitik {{nowrap|(2, 1)}}, {{nowrap|(4, 2)}}, anddan {{nowrap|(8, 3)}}, depicting,yang e.g.,menggambarkan {{math|log<sub>2</sub>(8) {{=}} 3}} anddan {{math|2<sup>3</sup> {{=}} 8}}. TheGrafik graphsecara getsarbiter arbitrarily close to themendekati sumbu-{{mvar|y}}-axis, buttetapi [[asymptoticasimptotik|does not meet ittak-memenuhinya]].]]
[[AdditionPenjumlahan]], [[multiplicationperkalian]], anddan [[exponentiationeksponen]] areadalah threetiga ofdari theoperasi mostaritmetika fundamentalyang arithmeticpaling operationsmendasar. TheKebalikan inversedari ofpenjumlahan additionadalah is subtractionpengurangan, and thedan inversekebalikan ofdari multiplicationperkalian isadalah [[divisionpembagian (mathematicsmatematika)|divisionpembagian]]. SimilarlySehingga, alogaritma logarithmsadalah isoperasi thekebalikan inverse operation ofdari [[exponentiationeksponen]]. ExponentiationEksponen isadalah whenketika asuatu numberbilangan {{mvar|b}}, the ''basebasis'' isdipangkatkan raisedke topangkat a certain powertertentu {{mvar|y}}, the ''exponenteksponen'' foruntuk givingmemberikan a valuenilai {{mvar|x}}; this denoteddilambangkan
: <math>b^y=x.</math>
For exampleMisalnya, raisingdipangkatkan {{math|2}} toke the power ofpangkat {{math|3}} givesmenghasilkan {{math|8}}, adalah: <math>2^3 = 8</math>
TheLogaritma logarithm of basebasis {{mvar|b}} is theadalah inverseoperasi operationkebalikan, thatyang providesmemberikan the outputkeluaran {{mvar|y}} from thedari inputmasukan {{mvar|x}}. That isArtinya, <math>y = \log_b x</math> issama equivalent todengan <math>x=b^y</math> ifjika {{mvar|b}} is a positiveadalah [[bilangan real number]] positif. (IfJika {{mvar|b}} indalam notbukan a positivebilangan real numberpositif, botheksponensial exponentiationdan andlogaritma logarithm can be defineddidefinisikan, buttetapi maymungkin takememerlukan severalbeberapa valuesnilai, whichyang makesmembuat definitionsdefinisi muchmenjadi morelebih complicaterumit.)
Salah satu motivasi historis utama memperkenalkan rumus logaritma adalah
One of the main historical motivations of introducing logarithms is the formula
:<math>\log_b(xy)=\log_b x + \log_b y,</math>
yang memungkinkan (sebelum ditemukannya komputer) untuk mengurangi perhitungan perkalian dan pembagian menjadi penambahan, pengurangan dan pencarian [[tabel logaritma]].
which allowed (before the invention of computers) reducing computation of multiplications and divisions to additions, subtractions and [[logarithm table|logarithm table]] looking.
== Definition ==
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