Question

How do I find the inverse of `e^x`?

Answer 1

The answer is `y=ln x`.

We find the answer the same way we find any inverse; we swap `x` and `y` then solve.

`y=e^x`
`x=e^y` swap
`ln x=ln (e^y)` take logarithm of both sides
`ln x=y`

`ln` and `e` functions cancel each other because they are inverses.