Solve 2^2*2^n=(2^4)^3

$$2 ^ { 2 } \times 2 ^ { n } = ( 2 ^ { 4 } ) ^ { 3 }$$

Solve for n

$$n=10$$

Steps Using Definition of Logarithm

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

$$4\times 2^{n}=4096$$

Divide both sides by 4.

$$2^{n}=1024$$

Take the logarithm of both sides of the equation.

$$\log(2^{n})=\log(1024)$$

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

$$n\log(2)=\log(1024)$$

Divide both sides by \log(2).

$$n=\frac{\log(1024)}{\log(2)}$$

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

$$n=\log_{2}\left(1024\right)$$