Solve quade^-x=8

$$\quad e ^ { - x } = 8$$

Solve for x

$$x=-3\ln(2)\approx -2.079441542$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$e^{-x}=8$$

Take the logarithm of both sides of the equation.

$$\log(e^{-x})=\log(8)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$-x\log(e)=\log(8)$$

Divide both sides by \log(e).

$$-x=\frac{\log(8)}{\log(e)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$-x=\log_{e}\left(8\right)$$

Divide both sides by -1.

$$x=\frac{3\ln(2)}{-1}$$

Solve for x (complex solution)

$$x=-2\pi n_{1}i-3\ln(2)$$

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