Hello I am having difficulty solving this question. Any help would be greatly appreciated.

$\displaystyle g(x)=3+x+e^x$

The e is the mathematical constant not a variable

find $\displaystyle g^{-1}(4)$

So I must find a value of x where g(x)=4

this is my attempt:

$\displaystyle 4=3+x+e^x$

$\displaystyle 1=x+e^x$

$\displaystyle 1-x=e^x$

I know that ln(e^x)=x so I thought of doing that

ln(1-x)=x

But I don't know what to do after that. Thanks for the assistance.