Solve 81^x=3^16

$$81 ^ { x } = 3 ^ { 16 }$$

Solve for x

$$x=4$$

Steps Using Definition of Logarithm

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

$$81^{x}=43046721$$

Take the logarithm of both sides of the equation.

$$\log(81^{x})=\log(43046721)$$

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

$$x\log(81)=\log(43046721)$$

Divide both sides by \log(81).

$$x=\frac{\log(43046721)}{\log(81)}$$

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

$$x=\log_{81}\left(43046721\right)$$

Solve for x (complex solution)

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

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