Solve lambdaw=e^x

$$\lambda w = e ^ { x }$$

Solve for w

$$w=\frac{e^{x}}{\lambda }$$

$$\lambda \neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\lambda w=e^{x}$$

Divide both sides by \lambda .

$$\frac{\lambda w}{\lambda }=\frac{e^{x}}{\lambda }$$

Dividing by \lambda undoes the multiplication by \lambda .

$$w=\frac{e^{x}}{\lambda }$$

Solve for x (complex solution)

$$x=\ln(w\lambda )+2\pi n_{1}i$$

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

$$w\neq 0\text{ and }\lambda \neq 0$$

Solve for x

$$x=\ln(w\lambda )$$

$$\left(\lambda <0\text{ and }w<0\right)\text{ or }\left(\lambda >0\text{ and }w>0\right)$$