Thank you!

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- Nov 25th 2012, 09:14 PMDima110If my equation is a^b=c, how do I get b by itself?
Thank you!

- Nov 25th 2012, 09:23 PMduckyoneRe: If my equation is a^b=c, how do I get b by itself?
i believe you'd use logarithms

Working with Exponents and Logarithms - Nov 25th 2012, 09:24 PMDima110Re: If my equation is a^b=c, how do I get b by itself?
I have been using natural logs. I've been using the equation f(x) = a*e^bx but I'm not sure if that is even the right equation or if I've been doing the work correctly.

- Nov 25th 2012, 10:13 PMMarkFLRe: If my equation is a^b=c, how do I get b by itself?
$\displaystyle a^b=c$ implies $\displaystyle \log_a(c)=b$.

- Nov 25th 2012, 10:26 PMProve ItRe: If my equation is a^b=c, how do I get b by itself?
Method 1: Use a logarithm of base a.

$\displaystyle \displaystyle \begin{align*} a^b &= c \\ \log_a{\left( a^b \right)} &= \log_a{(c)} \\ b &= \log_a{(c)} \end{align*}$

Method 2: Use a logarithm of ANY base.

$\displaystyle \displaystyle \begin{align*} a^b &= c \\ \log_k{\left( a^b \right)} &= \log_k{\left( c \right)} \\ b \log_k{(a)} &= \log_k{(c)} \\ b &= \frac{\log_k{(c)}}{\log_k{(a)}} \end{align*}$