Question

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

Answer 1

I found: `g(x)=log_3(x)`

Explanation:

You can take the log in base 3 of both sides to isolate `x` as:
`log_3(f(x))=log_3(3^x)` where we can cancel `log_3` with`3`;
So:
`log_3(f(x))=x`
This can be written as the inverse function changing `x` with `g(x)` and `f(x)` with `x` as:
`g(x)=log_3(x)`