$N=\log_{a}\left(x\right)$
$x>0\text{ and }a\neq 1\text{ and }a>0$

$\left\{\begin{matrix}a=x^{\frac{1}{N}}\text{, }&N\neq 0\text{ and }x\neq 1\text{ and }x>0\text{ and }x^{\frac{1}{N}}-1\neq 0\\a\in \left(0,1\right)\cup \left(1,\infty\right)\text{, }&x=1\text{ and }N=0\end{matrix}\right.$