# What is the inverse of f(x) = 3^x ?

Nov 2, 2015

I found: $g \left(x\right) = {\log}_{3} \left(x\right)$

#### Explanation:

You can take the log in base 3 of both sides to isolate $x$ as:
${\log}_{3} \left(f \left(x\right)\right) = {\log}_{3} \left({3}^{x}\right)$ where we can cancel ${\log}_{3}$ with$3$;
So:
${\log}_{3} \left(f \left(x\right)\right) = x$
This can be written as the inverse function changing $x$ with $g \left(x\right)$ and $f \left(x\right)$ with $x$ as:
$g \left(x\right) = {\log}_{3} \left(x\right)$