Solve (5)^frac{r{3}}=125

$$( 5 ) ^ { \frac { r } { 3 } } = 125$$

Solve for r

$$r=9$$

Steps Using Definition of Logarithm

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

$$5^{\frac{1}{3}r}=125$$

Take the logarithm of both sides of the equation.

$$\log(5^{\frac{1}{3}r})=\log(125)$$

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

$$\frac{1}{3}r\log(5)=\log(125)$$

Divide both sides by \log(5).

$$\frac{1}{3}r=\frac{\log(125)}{\log(5)}$$

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

$$\frac{1}{3}r=\log_{5}\left(125\right)$$

Multiply both sides by 3.

$$r=\frac{3}{\frac{1}{3}}$$