Solve xe^y-2x=5

$$x e ^ { y } - 2 x = 5$$

Solve for x (complex solution)

$$x=\frac{5}{e^{y}-2}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }y=\ln(2)+2\pi n_{1}i$$

Steps for Solving Linear Equation

Combine all terms containing x.

$$\left(e^{y}-2\right)x=5$$

Divide both sides by e^{y}-2.

$$\frac{\left(e^{y}-2\right)x}{e^{y}-2}=\frac{5}{e^{y}-2}$$

Dividing by e^{y}-2 undoes the multiplication by e^{y}-2.

$$x=\frac{5}{e^{y}-2}$$

Solve for x

$$x=\frac{5}{e^{y}-2}$$

$$y\neq \ln(2)$$

Steps for Solving Linear Equation

Combine all terms containing x.

$$\left(e^{y}-2\right)x=5$$

Divide both sides by e^{y}-2.

$$\frac{\left(e^{y}-2\right)x}{e^{y}-2}=\frac{5}{e^{y}-2}$$

Dividing by e^{y}-2 undoes the multiplication by e^{y}-2.

$$x=\frac{5}{e^{y}-2}$$

Solve for y (complex solution)

$$y=2\pi n_{1}i+\ln(2+\frac{5}{x})$$

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

$$x\neq -\frac{5}{2}\text{ and }x\neq 0$$

Solve for y

$$y=\ln(2+\frac{5}{x})$$

$$x>0\text{ or }x<-\frac{5}{2}$$