Solve pi^x=64

$$\pi ^ { x } = 64$$

Solve for x

$$x=6\log_{\pi }\left(2\right)\approx 3.633069368$$

Steps Using Definition of Logarithm

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

$$\pi ^{x}=64$$

Take the logarithm of both sides of the equation.

$$\log(\pi ^{x})=\log(64)$$

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

$$x\log(\pi )=\log(64)$$

Divide both sides by \log(\pi ).

$$x=\frac{\log(64)}{\log(\pi )}$$

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

$$x=\log_{\pi }\left(64\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\pi )}+6\log_{\pi }\left(2\right)$$

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