Solve zeta^5x=70

$$\zeta ^ { 5 x } = 70$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{5\ln(\zeta )}+\frac{\log_{\zeta }\left(70\right)}{5}$$

$$n_{1}\in \mathrm{Z}$$

$$\zeta \neq 1\text{ and }\zeta \neq 0$$

Solve for ζ (complex solution)

$$\zeta =e^{-\frac{2\pi n_{1}\left(Im(x)+iRe(x)\right)}{5\left(\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}\right)}}\times 70^{-\frac{iIm(x)}{5\left(\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}\right)}}\times 1680700000^{\frac{Re(x)}{25\left(\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}\right)}}$$

$$n_{1}\in \mathrm{Z}$$

Solve for x

$$x=\frac{\log_{\zeta }\left(70\right)}{5}$$

$$\zeta \neq 1\text{ and }\zeta >0$$

Solve for ζ

$$\left\{\begin{matrix}\zeta =-70^{\frac{1}{5x}}\text{, }&x\neq 0\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\\\zeta =70^{\frac{1}{5x}}\text{, }&x\neq 0\end{matrix}\right.$$