Solve 2^2n=992

$$2 ^ { 2 n } = 992$$

Solve for n

$$n = \frac{\log_{2} {(31)} + 5}{2} \approx 4.977098155$$

Steps Using Definition of Logarithm

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

$$2^{2n}=992$$

Take the logarithm of both sides of the equation.

$$\log(2^{2n})=\log(992)$$

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

$$2n\log(2)=\log(992)$$

Divide both sides by \log(2).

$$2n=\frac{\log(992)}{\log(2)}$$

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

$$2n=\log_{2}\left(992\right)$$

Divide both sides by 2.

$$n=\frac{\log_{2}\left(992\right)}{2}$$