Solve y=exp(x)

$$y = \exp ( x )$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=\frac{y}{ex^{2}}\text{, }&x\neq 0\\p\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$y=ex^{2}p$$

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

$$ex^{2}p=y$$

Divide both sides by ex^{2}.

$$\frac{ex^{2}p}{ex^{2}}=\frac{y}{ex^{2}}$$

Dividing by ex^{2} undoes the multiplication by ex^{2}.

$$p=\frac{y}{ex^{2}}$$

Solve for p

$$\left\{\begin{matrix}p=\frac{y}{ex^{2}}\text{, }&x\neq 0\\p\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$y=ex^{2}p$$

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

$$ex^{2}p=y$$

Divide both sides by ex^{2}.

$$\frac{ex^{2}p}{ex^{2}}=\frac{y}{ex^{2}}$$

Dividing by ex^{2} undoes the multiplication by ex^{2}.

$$p=\frac{y}{ex^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\left(ep\right)^{-\frac{1}{2}}\sqrt{y}\text{; }x=\left(ep\right)^{-\frac{1}{2}}\sqrt{y}\text{, }&p\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }p=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{\frac{y}{ep}}\text{; }x=-\sqrt{\frac{y}{ep}}\text{, }&\left(y\geq 0\text{ and }p>0\right)\text{ or }\left(y\leq 0\text{ and }p<0\right)\\x\in \mathrm{R}\text{, }&y=0\text{ and }p=0\end{matrix}\right.$$