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| − | ===[[ | + | ===[[Logarithm]]=== |
| − | + | {{WotWAlso}} | |
| + | '''Logarithms''' and [[exponents]] are very closely related. In fact, they are [[Function/Introduction#The_Inverse_of_a_Function|inverse]] [[function]]s. This means that logarithms can be used to reverse the result of exponentiation and vice versa, just as addition can be used to reverse the result of subtraction. Thus, if we have <math> a^x = b </math>, then taking the logarithm with base <math> a</math> on both sides will give us <math>x=\log_a{b}</math>. | ||
| − | + | We would read this as "the logarithm of b, base a, is x". For example, we know that <math>3^4=81</math>. To express the same fact... [[Logarithm|[more]]] | |
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Revision as of 20:07, 3 December 2007
Logarithm
This article was also a AoPSWiki word of the week
Logarithms and exponents are very closely related. In fact, they are inverse functions. This means that logarithms can be used to reverse the result of exponentiation and vice versa, just as addition can be used to reverse the result of subtraction. Thus, if we have
, then taking the logarithm with base
on both sides will give us
.
We would read this as "the logarithm of b, base a, is x". For example, we know that
. To express the same fact... [more]
, then taking the logarithm with base 
on both sides will give us 
.
. To express the same fact... 
