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.
Asked
Active
Viewed 1,135 times
1
-
Do you want to simplify this expression or do you want to find the inverse function? – StackTD Feb 02 '16 at 16:15
-
If $y=\ln(e^x-4)$, then $e^x-4=e^y$, so $e^x=e^y+4$ and $x=\ln(e^y+4)$ – egreg Feb 02 '16 at 16:15
1 Answers
4
Take each side to the power of $e$, then modify to solve for $x$:
$$\ln(e^x - 4) = y$$
$$\iff e^x - 4 = e^y$$
$$\iff e^x = e^y + 4$$
$$\iff x = \ln(e^y + 4)$$
adjan
- 5,741