Is possible to simplify $P = N^{ CN + 1}$ in terms of $N$? Having: $P = N^{CN + 1}$;
How can I simplify this equation to $N = \cdots$?
I tried using logarithms but I'm stucked...
Any ideas?

The equation $P=N^N$ doesn't have an elementary solution, but taking logarithms you can find approximate solutions (or even solutions in the form of transseries). In your case, take logarithms to find $(cn+1)\log n = p$. Assuming $p$ and so $n$ are large, $n\log n \approx p/c$. Therefore $n \approx p/c$, and so $$n \approx \frac{p/c}{\log (p/c)}.$$
Edit: the following is wrong, as J.M. pointed out.
Again ignoring the $1$ in the exponent, we have $P^{1/c} = N^N$ and so $N = W(P^{1/c})$, where $W$ is the Lambert function (see Wikipedia).
