Solve 3^-5x=81

$$3 ^ { - 5 x } = 81$$

Solve for x

$$x=-\frac{4}{5}=-0.8$$

Steps Using Definition of Logarithm

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

$$3^{-5x}=81$$

Take the logarithm of both sides of the equation.

$$\log(3^{-5x})=\log(81)$$

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

$$-5x\log(3)=\log(81)$$

Divide both sides by \log(3).

$$-5x=\frac{\log(81)}{\log(3)}$$

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

$$-5x=\log_{3}\left(81\right)$$

Divide both sides by -5.

$$x=\frac{4}{-5}$$

Solve for x (complex solution)

$$x=-\frac{i\times 2\pi n_{1}}{5\ln(3)}-\frac{4}{5}$$

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