Solve 36^2r*1/36=216

$$36 ^ { 2 r } \cdot \frac { 1 } { 36 } = 216$$

Solve for r

$$r = \frac{5}{4} = 1\frac{1}{4} = 1.25$$

Steps Using Definition of Logarithm

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

$$\frac{1}{36}\times 36^{2r}=216$$

Multiply both sides by 36.

$$36^{2r}=7776$$

Take the logarithm of both sides of the equation.

$$\log(36^{2r})=\log(7776)$$

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

$$2r\log(36)=\log(7776)$$

Divide both sides by \log(36).

$$2r=\frac{\log(7776)}{\log(36)}$$

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

$$2r=\log_{36}\left(7776\right)$$

Divide both sides by 2.

$$r=\frac{\frac{5}{2}}{2}$$