What is $\ln(e^x -4) $, solving for the inverse?

Question

What is $\ln(e^x -4) $, solving for the inverse? I know $\ln(e^x)$ is just $x$, but I don't know what to do with the 4.

Answer 1

Take each side to the power of $e$, then modify to solve for $x$:

$$\ln(e^x - 4) = y$$

$$\iff e^x - 4 = e^y$$

$$\iff e^x = e^y + 4$$

$$\iff x = \ln(e^y + 4)$$