Solve x=alphaB_{1}x^k

$$x = \alpha B _ { 1 } x ^ { k }$$

Solve for B_1 (complex solution)

$$\left\{\begin{matrix}B_{1}=\frac{x^{1-k}}{\alpha }\text{, }&\alpha \neq 0\text{ and }\left(k=0\text{ or }x\neq 0\right)\\B_{1}\in \mathrm{C}\text{, }&\left(k\neq 0\text{ or }\alpha =0\right)\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\alpha B_{1}x^{k}=x$$

The equation is in standard form.

$$\alpha x^{k}B_{1}=x$$

Divide both sides by \alpha x^{k}.

$$\frac{\alpha x^{k}B_{1}}{\alpha x^{k}}=\frac{x}{\alpha x^{k}}$$

Dividing by \alpha x^{k} undoes the multiplication by \alpha x^{k}.

$$B_{1}=\frac{x}{\alpha x^{k}}$$

Divide x by \alpha x^{k}.

$$B_{1}=\frac{x^{1-k}}{\alpha }$$

Solve for B_1

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

Steps for Solving Linear Equation

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

$$\alpha B_{1}x^{k}=x$$

The equation is in standard form.

$$\alpha x^{k}B_{1}=x$$

Divide both sides by \alpha x^{k}.

$$\frac{\alpha x^{k}B_{1}}{\alpha x^{k}}=\frac{x}{\alpha x^{k}}$$

Dividing by \alpha x^{k} undoes the multiplication by \alpha x^{k}.

$$B_{1}=\frac{x}{\alpha x^{k}}$$

Divide x by \alpha x^{k}.

$$B_{1}=\frac{x^{1-k}}{\alpha }$$

Solve for k (complex solution)

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

Solve for k

$$\left\{\begin{matrix}k=\log_{x}\left(\frac{x}{B_{1}\alpha }\right)\text{, }&B_{1}\alpha \neq 0\text{ and }x>0\text{ and }\left(\alpha >0\text{ or }B_{1}<0\right)\text{ and }\left(B_{1}>0\text{ or }\alpha <0\right)\text{ and }x\neq 1\\k\in \mathrm{R}\text{, }&|x|=1\text{ and }\alpha =\frac{1}{B_{1}}\text{ and }\left(Denominator(k)\text{bmod}2=1\text{ or }x=1\right)\text{ and }\left(Numerator(k)\text{bmod}2=1\text{ or }x=1\right)\text{ and }B_{1}\neq 0\\k>0\text{, }&\left(x=0\text{ and }B_{1}=0\right)\text{ or }\left(B_{1}\neq 0\text{ and }x=0\text{ and }\alpha =0\right)\text{ or }\left(B_{1}\alpha \neq 0\text{ and }x=0\right)\end{matrix}\right.$$