Solve 3^-p-2=27

$$3 ^ { - p - 2 } = 27$$

Solve for p

$$p=-5$$

Steps Using Definition of Logarithm

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

$$3^{-p-2}=27$$

Take the logarithm of both sides of the equation.

$$\log(3^{-p-2})=\log(27)$$

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

$$\left(-p-2\right)\log(3)=\log(27)$$

Divide both sides by \log(3).

$$-p-2=\frac{\log(27)}{\log(3)}$$

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

$$-p-2=\log_{3}\left(27\right)$$

Add 2 to both sides of the equation.

$$-p=3-\left(-2\right)$$

Divide both sides by -1.

$$p=\frac{5}{-1}$$