Solve 16^2n=64

$$16 ^ { 2 n } = 64$$

Solve for n

$$n=\frac{3}{4}=0.75$$

Steps Using Definition of Logarithm

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

$$16^{2n}=64$$

Take the logarithm of both sides of the equation.

$$\log(16^{2n})=\log(64)$$

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

$$2n\log(16)=\log(64)$$

Divide both sides by \log(16).

$$2n=\frac{\log(64)}{\log(16)}$$

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

$$2n=\log_{16}\left(64\right)$$

Divide both sides by 2.

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