Solve 3x=θ{(e)^8y}

$$3x= \theta {(e)^{ 8y }}$$

Solve for x

$$x=\frac{\theta e^{8y}}{3}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$3x=\theta e^{8y}$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{\theta e^{8y}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{\theta e^{8y}}{3}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{\pi n_{1}i}{4}+\frac{\ln(\frac{x}{\theta })+\ln(3)}{8}\text{, }n_{1}\in \mathrm{Z}\text{, }&x\neq 0\text{ and }\theta \neq 0\\y\in \mathrm{C}\text{, }&x=0\text{ and }\theta =0\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y=\frac{\ln(\frac{x}{\theta })+\ln(3)}{8}\text{, }&\left(x<0\text{ and }\theta <0\right)\text{ or }\left(x>0\text{ and }\theta >0\right)\\y\in \mathrm{R}\text{, }&x=0\text{ and }\theta =0\end{matrix}\right.$$