Solve e=mc^v

$$e = m c ^ { v }$$

Solve for m (complex solution)

$$m=\frac{e}{c^{v}}$$

$$v=0\text{ or }c\neq 0$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$mc^{v}=e$$

The equation is in standard form.

$$c^{v}m=e$$

Divide both sides by c^{v}.

$$\frac{c^{v}m}{c^{v}}=\frac{e}{c^{v}}$$

Dividing by c^{v} undoes the multiplication by c^{v}.

$$m=\frac{e}{c^{v}}$$

Solve for m

$$m=\frac{e}{c^{v}}$$

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

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$mc^{v}=e$$

The equation is in standard form.

$$c^{v}m=e$$

Divide both sides by c^{v}.

$$\frac{c^{v}m}{c^{v}}=\frac{e}{c^{v}}$$

Dividing by c^{v} undoes the multiplication by c^{v}.

$$m=\frac{e}{c^{v}}$$

Solve for c (complex solution)

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

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

$$m\neq 0$$

Solve for c

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