How to calculate inverse of $y=3x+4\log(x+1)$?

Question

How to calculate inverse of $y=3x+4 \log(x+1)$?

Wolframalpha says that

http://m.wolframalpha.com/input/?i=Inverse+3x%2B4+log%28x%2B1%29+&x=0&y=0

Answer 1

As I wrote in a comment, let us simplify notations using $z=y+3$ and $t=x+1$. This makes the equation to be $$z=3t+4\log(t)$$ that is to say $$z=\log(t^4\,e^{3t})\implies e^z=t^4 e^{3t}\implies e^{\frac z4}=t\,e^{\frac{3t}4}$$ So $$\frac 34 e^{\frac z4}=\frac{3t}4 \,e^{\frac{3t}4}$$

I am sure that you can take it from here.

You must take care about the fact that this is one of the four possible solutions (I raised things to power $\frac 14$).