Question

How do you find the inverse of `f(x) =10^x`?

Answer 1

`f^(-1)(x)=logx`

Explanation:

By definition, `y=f^(-1)(x)ifff(y)=x`
`iff 10^y=x`
We can now take log base 10 on both sides and use laws of logs to yield
`y=log_10x`

I will also show the graphs of both f and its inverse for clarity.

graph{10^x [-6.37, 6.12, -2.67, 3.57]}

graph{logx [-2.26, 6.514, -2.257, 2.126]}