Find an expression for z as a function of w in terms of the complex logarithm where

$\displaystyle w = f(z) := 2exp(z) + exp(2z)$

and z is complex.

I assume I need to get f(z) into a form that I can take logs, but I'm really struggling with getting started on this one.

I know that the answer is $\displaystyle z = log(-1 + exp(\frac{1}{2} log(1+w)))$.

Any help would be awsome.