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

Thank you!

2. ## 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

3. ## 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.

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

$a^b=c$ implies $\log_a(c)=b$.

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

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*}