# If my equation is a^b=c, how do I get b by itself?

• November 25th 2012, 10:14 PM
Dima110
If my equation is a^b=c, how do I get b by itself?
Thank you!
• November 25th 2012, 10:23 PM
duckyone
Re: 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
• November 25th 2012, 10:24 PM
Dima110
Re: 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.
• November 25th 2012, 11:13 PM
MarkFL
Re: If my equation is a^b=c, how do I get b by itself?
$a^b=c$ implies $\log_a(c)=b$.
• November 25th 2012, 11:26 PM
Prove It
Re: If my equation is a^b=c, how do I get b by itself?
Quote:

Originally Posted by Dima110
Thank you!

Method 1: Use a logarithm of base a.

\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 \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*}