How to find the inverse of a function involving e with a coefficient?

Question

I was wondering how I would find the inverse of the following function, since the e has a co-efficient:

$\frac{e^x}{1+2e^x}=y$

I got as far as $\ln y+\ln(2e^x) = \ln e^x$, which would be changed into:

$\ln y + \ln(2e^x) = x\ln e$ (or just $x$)

But where do I go from here?

Answer 1

$\frac{e^x}{1+2e^x}=\frac1{e^{-x}+2}$, so $e^{-x}=\frac1y-2$.