Solve y=(m+1/2m-3)^x*k

$$y = ( \frac { m + 1 } { 2 m - 3 } ) ^ { x } \cdot k$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=\frac{y}{\left(\frac{m+1}{2m-3}\right)^{x}}\text{, }&\left(x=0\text{ or }m\neq -1\right)\text{ and }m\neq \frac{3}{2}\\k\in \mathrm{C}\text{, }&m=-1\text{ and }x\neq 0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\left(\frac{m+1}{2m-3}\right)^{x}k=y$$

Divide both sides by \left(\left(m+1\right)\left(2m-3\right)^{-1}\right)^{x}.

$$\frac{\left(\frac{m+1}{2m-3}\right)^{x}k}{\left(\frac{m+1}{2m-3}\right)^{x}}=\frac{y}{\left(\frac{m+1}{2m-3}\right)^{x}}$$

Dividing by \left(\left(m+1\right)\left(2m-3\right)^{-1}\right)^{x} undoes the multiplication by \left(\left(m+1\right)\left(2m-3\right)^{-1}\right)^{x}.

$$k=\frac{y}{\left(\frac{m+1}{2m-3}\right)^{x}}$$

Solve for k

$$\left\{\begin{matrix}k=\frac{y}{\left(\frac{m+1}{2m-3}\right)^{x}}\text{, }&\left(Denominator(x)\text{bmod}2=1\text{ and }m<\frac{3}{2}\text{ and }m>-1\right)\text{ or }m<-1\text{ or }m>\frac{3}{2}\\k\in \mathrm{R}\text{, }&y=0\text{ and }m=-1\text{ and }x>0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\left(\frac{m+1}{2m-3}\right)^{x}k=y$$

Divide both sides by \left(\left(m+1\right)\left(2m-3\right)^{-1}\right)^{x}.

$$\frac{\left(\frac{m+1}{2m-3}\right)^{x}k}{\left(\frac{m+1}{2m-3}\right)^{x}}=\frac{y}{\left(\frac{m+1}{2m-3}\right)^{x}}$$

Dividing by \left(\left(m+1\right)\left(2m-3\right)^{-1}\right)^{x} undoes the multiplication by \left(\left(m+1\right)\left(2m-3\right)^{-1}\right)^{x}.

$$k=\frac{y}{\left(\frac{m+1}{2m-3}\right)^{x}}$$