If $\displaystyle f(x)=2x+ln x$, find $\displaystyle f^{-1}(2)$.

I keep getting stuck trying to get the inverse. Here's what i got:

$\displaystyle y=2x+lnx$

$\displaystyle -e^{lnx}+e^y=e^{2x}$

$\displaystyle -x+e^y=e^{2x}$

Then i don't know what to do, and i feel like i'm approaching it incorrectly.

So, i tried: $\displaystyle \frac{y}{2x}=lnx$

$\displaystyle x=e^{\frac{y}{2x}}$ and i'm still not getting anywhere.

Any help would be mucho appriciated!