Solve x^n-1(1/2x^2)^r=x

$$x ^ { n - 1 } ( \frac { 1 } { 2 x ^ { 2 } } ) ^ { r } = x$$

Solve for n

$$\left\{\begin{matrix}n=\frac{\ln(\frac{x}{\left(\frac{1}{2x^{2}}\right)^{r}})+\ln(x)}{\ln(x)}\text{, }&x>0\text{ and }x\neq 1\text{ and }\left(\frac{1}{2x^{2}}\right)^{r}\neq 0\\n\in \mathrm{R}\text{, }&\left(r=0\text{ and }x=1\right)\text{ or }\left(x=-1\text{ and }r=0\text{ and }Numerator(n-1)\text{bmod}2=1\text{ and }Denominator(n)\text{bmod}2=1\right)\end{matrix}\right.$$

Solve for r

$$\left\{\begin{matrix}r=-\frac{\left(2-n\right)\ln(x)}{\ln(x^{2})+\ln(2)}\text{, }&\left(x>0\text{ and }x\neq \frac{\sqrt{2}}{2}\right)\text{ or }\left(x^{2-n}>0\text{ and }x\neq -\frac{\sqrt{2}}{2}\text{ and }x<0\text{ and }Denominator(n)\text{bmod}2=1\right)\\r\in \mathrm{R}\text{, }&n=2\text{ and }|x|=\frac{\sqrt{2}}{2}\end{matrix}\right.$$