Solve 4^3-p=16

$$4 ^ { 3 - p } = 16$$

Solve for p

$$p=1$$

Steps Using Definition of Logarithm

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

$$4^{-p+3}=16$$

Take the logarithm of both sides of the equation.

$$\log(4^{-p+3})=\log(16)$$

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

$$\left(-p+3\right)\log(4)=\log(16)$$

Divide both sides by \log(4).

$$-p+3=\frac{\log(16)}{\log(4)}$$

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

$$-p+3=\log_{4}\left(16\right)$$

Subtract 3 from both sides of the equation.

$$-p=2-3$$

Divide both sides by -1.

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