Eksponensiasi: Perbedaan antara revisi

[[ImageBerkas:Expo02.svg|thumb|315px|Grafik dari {{nowrap|1=''y'' = ''b''^''x''}} untuk beberapa basis ''b'': [[#Pemangkatan sepuluh|basis&nbsp;10]] (<span style="color:green">hijau</span>), [[#Fungsi eksponensial|basis&nbsp;''e'']] (<span style="color:red">merah</span>), [[#Pemangkatan dua|basis&nbsp;2]] (<span style="color:blue">biru</span>), dan basis&nbsp;{{sfrac|2}} (<span style="color:cyan">cyan</span>). Setiap kurva melalui titik {{nowrap|(0, 1)}} karena setiap bilangan bukan nol dipangkatkan 0 adalah 1. Pada {{nowrap|1=''x'' = 1}}, nilai ''y'' sama dengan basis karena setiap bilangan dipangkatkan 1 adalah bilangan itu sendiri.]]

Ekspresi ''b''³ = ''b''·''b''·''b'' disebut [[:en:Cube (algebra)|''cube'']] dari ''b'' karena [[volume]] suatu [[kubus]] dengan panjang sisi ''b'' adalah ''b''³. Diucapkan "b pangkat tiga" ({{lang-en|b cubed}}).

* [http://jeff560.tripod.com/e.html Earliest Known Uses of Some of the Words of Mathematics]

* Michael Stifel, ''Arithmetica integra'' (Nuremberg ("Norimberga"), (Germany): Johannes Petreius, 1544), Liber III (Book 3), Caput III (Chapter 3): De Algorithmo numerorum Cossicorum. (On algorithms of algebra.), [http://books.google.com/books?id=fndPsRv08R0C&vq=exponens&pg=RA7-PA231#v=onepage&q&f=false page 236.] Stifel was trying to conveniently represent the terms of geometric progressions. He devised a cumbersome notation for doing that. On page 236, he presented the notation for the first eight terms of a geometric progression (using 1 as a base) and then he wrote: ''"Quemadmodum autem hic vides, quemlibet terminum progressionis cossicæ, suum habere exponentem in suo ordine (ut 1ze habet 1. 1ʓ habet 2 &c.) sic quilibet numerus cossicus, servat exponentem suæ denominationis implicite, qui ei serviat & utilis sit, potissimus in multiplicatione & divisione, ut paulo inferius dicam."'' (However, you see how each term of the progression has its exponent in its order (as 1ze has a 1, 1ʓ has a 2, etc.), so each number is implicitly subject to the exponent of its denomination, which [in turn] is subject to it and is useful mainly in multiplication and division, as I will mention just below.) [Note: Most of Stifel's cumbersome symbols were taken from [[Christoff Rudolff]], who in turn took them from Leonardo Fibonacci's ''Liber Abaci'' (1202), where they served as shorthand symbols for the Latin words ''res/radix'' (x), ''census/zensus'' (x²), and ''cubus'' (x³).]</ref>

Notasi eksponensiasi modern diperkenalkan oleh [[René Descartes]] dalam karyanya ''Géométrie'' pada tahun 1637.<ref name = Descartes>René Descartes, ''Discourse de la Méthode'' … (Leiden, (Netherlands): Jan Maire, 1637), appended book: ''La Géométrie'', book one, [http://gallica.bnf.fr/ark:/12148/btv1b86069594/f383.image page 299.] From page 299: ''" … Et ''aa'', ou ''a''², pour multiplier ''a'' par soy mesme; Et ''a''³, pour le multiplier encore une fois par ''a'', & ainsi a l'infini ; … "'' ( … and ''aa'', or ''a''², in order to multiply ''a'' by itself; and ''a''³, in order to multiply it once more by ''a'', and thus to infinity ; … )</ref><ref>{{cite book|title=A History of Mathematics|url=http://books.google.com/books?id=mGJRjIC9fZgC&pg=PA178|first=Florian|last=Cajori|edition=5th|year=1991|page=178|origyear=1893|publisher=AMS|isbn=0821821024}}</ref>

== Lihat pula ==

* [[Peluruhan eksponensial]]

== Bacaan lebih lanjut ==

== Referensi ==

== Pranala luar ==

* {{planetmath reference|id=3948|title=Introducing 0th power}}