Solve 2^2x-4=256

$${ 2 }^{ 2x-4 } = 256$$

Solve for x

$$x=6$$

Steps Using Definition of Logarithm

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

$$2^{2x-4}=256$$

Take the logarithm of both sides of the equation.

$$\log(2^{2x-4})=\log(256)$$

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

$$\left(2x-4\right)\log(2)=\log(256)$$

Divide both sides by \log(2).

$$2x-4=\frac{\log(256)}{\log(2)}$$

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

$$2x-4=\log_{2}\left(256\right)$$

Add 4 to both sides of the equation.

$$2x=8-\left(-4\right)$$

Divide both sides by 2.

$$x=\frac{12}{2}$$