Solve 6^-3n-3=216

$$6 ^ { - 3 n - 3 } = 216$$

Solve for n

$$n=-2$$

Steps Using Definition of Logarithm

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

$$6^{-3n-3}=216$$

Take the logarithm of both sides of the equation.

$$\log(6^{-3n-3})=\log(216)$$

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

$$\left(-3n-3\right)\log(6)=\log(216)$$

Divide both sides by \log(6).

$$-3n-3=\frac{\log(216)}{\log(6)}$$

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

$$-3n-3=\log_{6}\left(216\right)$$

Add 3 to both sides of the equation.

$$-3n=3-\left(-3\right)$$

Divide both sides by -3.

$$n=\frac{6}{-3}$$