Solve 36^-n=6^3

$$36 ^ { - n } = 6 ^ { 3 }$$

Solve for n

$$n = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps Using Definition of Logarithm

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

$$36^{-n}=216$$

Take the logarithm of both sides of the equation.

$$\log(36^{-n})=\log(216)$$

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

$$-n\log(36)=\log(216)$$

Divide both sides by \log(36).

$$-n=\frac{\log(216)}{\log(36)}$$

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

$$-n=\log_{36}\left(216\right)$$

Divide both sides by -1.

$$n=\frac{\frac{3}{2}}{-1}$$