Solve 2^x*2^2=2^4

$$2 ^ { x } \cdot 2 ^ { 2 } = 2 ^ { 4 }$$

Solve for x

$$x=2$$

Steps Using Definition of Logarithm

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

$$4\times 2^{x}=16$$

Divide both sides by 4.

$$2^{x}=4$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(4)$$

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

$$x\log(2)=\log(4)$$

Divide both sides by \log(2).

$$x=\frac{\log(4)}{\log(2)}$$

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

$$x=\log_{2}\left(4\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+2$$

$$n_{1}\in \mathrm{Z}$$