Solve 2^4-x=2^2

$$2 ^ { 4 - x } = 2 ^ { 2 }$$

Solve for x

$$x=2$$

Steps Using Definition of Logarithm

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

$$2^{-x+4}=4$$

Take the logarithm of both sides of the equation.

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

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

$$\left(-x+4\right)\log(2)=\log(4)$$

Divide both sides by \log(2).

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

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

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

Subtract 4 from both sides of the equation.

$$-x=2-4$$

Divide both sides by -1.

$$x=-\frac{2}{-1}$$

Solve for x (complex solution)

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

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