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{{Collapse bottom}}Adapun [[kalkulator ilmiah]] yang menghitung logaritma dengan bilangan pokok 10 dan {{mvar|[[e (mathematical constant)|e]]}}.<ref>{{Citation|last1=Bernstein|first1=Stephen|last2=Bernstein|first2=Ruth|title=Schaum's outline of theory and problems of elements of statistics. I, Descriptive statistics and probability|publisher=[[McGraw-Hill]]|location=New York|series=Schaum's outline series|isbn=978-0-07-005023-5|year=1999|url=https://archive.org/details/schaumsoutlineof00bern}}, hlm. 21</ref> Logaritma terhadap setiap bilangan pokok {{mvar|b}} dapat ditentukan menggunaka menggunakan kedua logaritma tersebut melalui rumus sebelumnya:
: <math> ^b\!\
Diberikan suatu bilangan {{mvar|x}} dan logaritma {{math|1=''y'' = log<sub>''b''</sub> ''x''}}, dengan {{mvar|b}} adalah bilangan pokok yang tidak diketahui. Bilangan pokok logaritma dapat dirumuskan sebagai
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The '''history of logarithms''' in seventeenth-century Europe is the discovery of a new [[Function (mathematics)|function]] that extended the realm of analysis beyond the scope of algebraic methods. The method of logarithms was publicly propounded by [[John Napier]] in 1614, in a book titled ''Mirifici Logarithmorum Canonis Descriptio'' (''Description of the Wonderful Rule of Logarithms'').<ref>{{citation|first=John|last=Napier|author-link=John Napier|title=Mirifici Logarithmorum Canonis Descriptio|trans-title=The Description of the Wonderful Rule of Logarithms|language=la|location=Edinburgh, Scotland|publisher=Andrew Hart|year=1614|url=http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN527914568&DMDID=DMDLOG_0001&LOGID=LOG_0001&PHYSID=PHYS_0001}}</ref><ref>{{Citation|first=Ernest William|last=Hobson|title=John Napier and the invention of logarithms, 1614|year=1914|publisher=The University Press|location=Cambridge|url=https://archive.org/details/johnnapierinvent00hobsiala}}</ref> Prior to Napier's invention, there had been other techniques of similar scopes, such as the [[prosthaphaeresis]] or the use of tables of progressions, extensively developed by [[Jost Bürgi]] around 1600.<ref name="folkerts">{{citation|last1=Folkerts|first1=Menso|last2=Launert|first2=Dieter|last3=Thom|first3=Andreas|arxiv=1510.03180|doi=10.1016/j.hm.2016.03.001|issue=2|journal=[[Historia Mathematica]]|mr=3489006|pages=133–147|title=Jost Bürgi's method for calculating sines|volume=43|year=2016|s2cid=119326088}}</ref><ref>{{mactutor|id=Burgi|title=Jost Bürgi (1552 – 1632)}}</ref> Napier coined the term for logarithm in Middle Latin, “logarithmus,” derived from the Greek, literally meaning, “ratio-number,” from ''logos'' “proportion, ratio, word” + ''arithmos'' “number”.▼
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The [[common logarithm]] of a number is the index of that power of ten which equals the number.<ref>William Gardner (1742) ''Tables of Logarithms''</ref> Speaking of a number as requiring so many figures is a rough allusion to common logarithm, and was referred to by [[Archimedes]] as the “order of a number”.<ref>{{citation|last=Pierce|first=R. C. Jr.|date=January 1977|doi=10.2307/3026878|issue=1|journal=[[The Two-Year College Mathematics Journal]]|jstor=3026878|pages=22–26|title=A brief history of logarithms|volume=8}}</ref> The first real logarithms were heuristic methods to turn multiplication into addition, thus facilitating rapid computation. Some of these methods used tables derived from trigonometric identities.<ref>Enrique Gonzales-Velasco (2011) ''Journey through Mathematics – Creative Episodes in its History'', §2.4 Hyperbolic logarithms, p. 117, Springer {{isbn|978-0-387-92153-2}}</ref> Such methods are called [[prosthaphaeresis]].▼
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Penemuan [[fungsi (matematika)|fungsi]] sekarang dikenal sebagai [[logaritma alami]] dimulai sebagai upaya untuk [[kuadratur (matematika)|kuadratur]] dari [[hiperbola]] persegi panjang oleh [[Grégoire de Saint-Vincent]], seorang Yesuit Belgia yang tinggal di Praha. Archimedes telah menulis ''[[The Quadrature of the Parabola]]'' pada abad ketiga SM, tetapi kuadratur untuk hiperbola menghindari semua upaya sampai Saint-Vincent menerbitkan hasilnya pada tahun 1647. Relasi yang disediakan logaritma antara [[barisan dan deret geometri]] dalam [[argumen dari sebuah fungsi|argumen]] dan nilai [[barisan dan deret aritmetika]], [[A. A. de Sarasa]] diminta untuk membuat hubungan kuadratur Saint-Vincent dan tradisi logaritma dalam [[prosthafaeresis]], mengarah ke istilah "logaritma hiperbolik", sebuah persamaan kata untuk logaritma alami. Dengan segera, fungsi baru tersebut dihargai oleh [[Christiaan Huygens]] dan [[James Gregory (matematikawan)|James Gregory]]. Notasi Log y diadopsi oleh [[Gottfried Wilhelm Leibniz|Leibniz]] pada tahun 1675,<ref>[[Florian Cajori]] (1913) "History of the exponential and logarithm concepts", [[American Mathematical Monthly]] 20: 5, 35, 75, 107, 148, 173, 205.</ref> dan tahun berikutnya dia mengaitkannya dengan [[kalkulus integral|integral]] <math display="inline">\int \frac{dy}{y} .</math>
Before Euler developed his modern conception of complex natural logarithms, [[Roger Cotes#Mathematics|Roger Cotes]] had a nearly equivalent result when he showed in 1714 that<ref>{{citation|last1=Stillwell|first1=J.|title=Mathematics and Its History|date=2010|publisher=Springer|edition=3rd}}</ref>▼
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== Tabel logaritma, kaidah geser, dan penerapan bersejarah ==
[[Berkas:Logarithms_Britannica_1797.png|ka|jmpl|360x360px|
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=== Log tables ===
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