Solve ne^-2x=40

$$n e ^ { - 2 x } = 40$$

Solve for n

$$n=40e^{2x}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{1}{e^{2x}}n=40$$

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

$$\frac{\frac{1}{e^{2x}}ne^{2x}}{1}=\frac{40e^{2x}}{1}$$

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

$$n=\frac{40e^{2x}}{1}$$

Divide 40 by e^{-2x}.

$$n=40e^{2x}$$

Solve for x (complex solution)

$$x=\frac{\ln(n)-\ln(40)}{2}-\pi n_{1}i$$

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

$$n\neq 0$$

Solve for x

$$x=\frac{\ln(n)+\ln(\frac{1}{40})}{2}$$

$$n>0$$