Solve E=L^c32^7

$$E = L ^ { c } 32 ^ { 7 }$$

Solve for E (complex solution)

$$E=34359738368L^{c}$$

Solve for L (complex solution)

$$L=2^{-\frac{35\left(Re(c)-iIm(c)\right)}{\left(Re(c)\right)^{2}+\left(Im(c)\right)^{2}}}e^{\frac{Im(c)arg(E)+iRe(c)arg(E)}{\left(Re(c)\right)^{2}+\left(Im(c)\right)^{2}}-\frac{2\pi n_{1}iRe(c)}{\left(Re(c)\right)^{2}+\left(Im(c)\right)^{2}}-\frac{2\pi n_{1}Im(c)}{\left(Re(c)\right)^{2}+\left(Im(c)\right)^{2}}}\left(|E|\right)^{\frac{Re(c)-iIm(c)}{\left(Re(c)\right)^{2}+\left(Im(c)\right)^{2}}}$$

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

Solve for E

$$E=34359738368L^{c}$$

$$\left(L<0\text{ and }Denominator(c)\text{bmod}2=1\right)\text{ or }\left(L=0\text{ and }c>0\right)\text{ or }L>0$$

Solve for L

$$\left\{\begin{matrix}L=\left(\frac{E}{34359738368}\right)^{\frac{1}{c}}\text{, }&\left(Numerator(c)\text{bmod}2=1\text{ and }Denominator(c)\text{bmod}2=1\text{ and }E<0\text{ and }\left(\frac{E}{34359738368}\right)^{\frac{1}{c}}\neq 0\right)\text{ or }\left(\left(\frac{E}{34359738368}\right)^{\frac{1}{c}}<0\text{ and }E>0\text{ and }c\neq 0\text{ and }Denominator(c)\text{bmod}2=1\right)\text{ or }\left(E=0\text{ and }c>0\right)\text{ or }\left(\left(\frac{E}{34359738368}\right)^{\frac{1}{c}}>0\text{ and }E>0\text{ and }c\neq 0\right)\\L=-\left(\frac{E}{34359738368}\right)^{\frac{1}{c}}\text{, }&\left(E<0\text{ and }Numerator(c)\text{bmod}2=1\text{ and }Numerator(c)\text{bmod}2=0\text{ and }Denominator(c)\text{bmod}2=1\text{ and }\left(\frac{E}{34359738368}\right)^{\frac{1}{c}}\neq 0\right)\text{ or }\left(E>0\text{ and }c\neq 0\text{ and }\left(\frac{E}{34359738368}\right)^{\frac{1}{c}}>0\text{ and }Numerator(c)\text{bmod}2=0\text{ and }Denominator(c)\text{bmod}2=1\right)\text{ or }\left(Numerator(c)\text{bmod}2=0\text{ and }E=0\text{ and }c>0\right)\text{ or }\left(E>0\text{ and }c\neq 0\text{ and }\left(\frac{E}{34359738368}\right)^{\frac{1}{c}}<0\text{ and }Numerator(c)\text{bmod}2=0\right)\\L\neq 0\text{, }&c=0\text{ and }E=34359738368\end{matrix}\right.$$