Question

$$x ^ { n } = n x ^ { n - 1 }$$

Solve for n (complex solution)

$\left\{\begin{matrix}\\n=x\text{, }&\text{unconditionally}\\n\neq 1\text{, }&x=0\end{matrix}\right.$

Solve for x (complex solution)

$\left\{\begin{matrix}\\x=n\text{, }&\text{unconditionally}\\x=0\text{, }&n\neq 1\end{matrix}\right.$

Solve for n

$\left\{\begin{matrix}n=x\text{, }&x>0\text{ or }\left(x<0\text{ and }Denominator(x)\text{bmod}2=1\right)\\n>1\text{, }&x=0\end{matrix}\right.$

Solve for x

$\left\{\begin{matrix}x=n\text{, }&n>0\text{ or }\left(n<0\text{ and }Denominator(n)\text{bmod}2=1\right)\\x=0\text{, }&n>1\end{matrix}\right.$