Solve y=(n/2)^-x

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

Solve for n (complex solution)

$$\left\{\begin{matrix}n=e^{-\frac{2\pi n_{1}iRe(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}-\frac{2\pi n_{1}Im(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}+\frac{arg(\frac{1}{y})Im(x)+iarg(\frac{1}{y})Re(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\left(|y|\right)^{\frac{-Re(x)+iIm(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\text{, }n_{1}\in \mathrm{Z}\text{, }&y\neq 0\\n=0\text{, }&x\neq 0\end{matrix}\right.$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{2\pi n_{1}i}{-\ln(n)+\ln(2)}+\frac{\ln(y)}{-\ln(n)+\ln(2)}\text{, }n_{1}\in \mathrm{Z}\text{, }&y\neq 0\text{ and }n\neq 2\text{ and }n\neq 0\\x\in \mathrm{C}\text{, }&\left(n=0\text{ and }y=0\right)\text{ or }\left(n=2\text{ and }y=1\right)\end{matrix}\right.$$

Solve for n

$$\left\{\begin{matrix}n=2\times \left(\frac{1}{y}\right)^{\frac{1}{x}}\text{, }&\left(Numerator(x)\text{bmod}2=1\text{ and }Denominator(x)\text{bmod}2=1\text{ and }\left(\frac{1}{y}\right)^{\frac{1}{x}}\neq 0\text{ and }y<0\right)\text{ or }\left(\left(\frac{1}{y}\right)^{\frac{1}{x}}>0\text{ and }x\neq 0\text{ and }y>0\right)\text{ or }\left(\left(\frac{1}{y}\right)^{\frac{1}{x}}<0\text{ and }x\neq 0\text{ and }Denominator(x)\text{bmod}2=1\text{ and }y>0\right)\\n=-2\times \left(\frac{1}{y}\right)^{\frac{1}{x}}\text{, }&\left(y<0\text{ and }Numerator(x)\text{bmod}2=1\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\text{ and }\left(\frac{1}{y}\right)^{\frac{1}{x}}\neq 0\right)\text{ or }\left(y>0\text{ and }x\neq 0\text{ and }\left(\frac{1}{y}\right)^{\frac{1}{x}}<0\text{ and }Numerator(x)\text{bmod}2=0\right)\text{ or }\left(y>0\text{ and }x\neq 0\text{ and }\left(\frac{1}{y}\right)^{\frac{1}{x}}>0\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\right)\\n\neq 0\text{, }&y=1\text{ and }x=0\end{matrix}\right.$$

Solve for x

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