Solve 3^20r-3^2=0

$$3 ^ { 20 r } - 3 ^ { 2 } = 0$$

Solve for r

$$r=\frac{1}{10}=0.1$$

Steps Using Definition of Logarithm

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

$$3^{20r}-9=0$$

Add 9 to both sides of the equation.

$$3^{20r}=9$$

Take the logarithm of both sides of the equation.

$$\log(3^{20r})=\log(9)$$

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

$$20r\log(3)=\log(9)$$

Divide both sides by \log(3).

$$20r=\frac{\log(9)}{\log(3)}$$

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

$$20r=\log_{3}\left(9\right)$$

Divide both sides by 20.

$$r=\frac{2}{20}$$