Solve pi^r=73

$$\pi ^ { r } = 73$$

Solve for r

$$r=\log_{\pi }\left(73\right)\approx 3.748010333$$

Steps Using Definition of Logarithm

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

$$\pi ^{r}=73$$

Take the logarithm of both sides of the equation.

$$\log(\pi ^{r})=\log(73)$$

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

$$r\log(\pi )=\log(73)$$

Divide both sides by \log(\pi ).

$$r=\frac{\log(73)}{\log(\pi )}$$

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

$$r=\log_{\pi }\left(73\right)$$

Solve for r (complex solution)

$$r=\frac{2\pi n_{1}i}{\ln(\pi )}+\log_{\pi }\left(73\right)$$

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