Solve 3^x=81

$$3 ^ { x } = 81$$

Solve for x

$$x=4$$

Steps Using Definition of Logarithm

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

$$3^{x}=81$$

Take the logarithm of both sides of the equation.

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

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

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

Divide both sides by \log(3).

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

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

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

Solve for x (complex solution)

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

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