Solve 2sqrt{3}+2i=x*e^2y

$$2 \sqrt { 3 } + 2 i = x \cdot e ^ { 2 y }$$

Solve for x

$$x=\frac{2\left(\sqrt{3}+i\right)}{e^{2y}}$$

Steps for Solving Linear Equation

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

$$xe^{2y}=2\sqrt{3}+2i$$

The equation is in standard form.

$$e^{2y}x=2\sqrt{3}+2i$$

Divide both sides by e^{2y}.

$$\frac{e^{2y}x}{e^{2y}}=\frac{2\sqrt{3}+2i}{e^{2y}}$$

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

$$x=\frac{2\sqrt{3}+2i}{e^{2y}}$$

Divide 2\sqrt{3}+2i by e^{2y}.

$$x=\frac{2\left(\sqrt{3}+i\right)}{e^{2y}}$$

Solve for y

$$y=\frac{\ln(\frac{\sqrt{3}+i}{x})+\ln(2)}{2}+\pi n_{1}i$$

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

$$x\neq 0$$