Solve 2^4x=256

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

Solve for x

$$x=2$$

Steps Using Definition of Logarithm

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

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

Take the logarithm of both sides of the equation.

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

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

$$4x\log(2)=\log(256)$$

Divide both sides by \log(2).

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

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

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

Divide both sides by 4.

$$x=\frac{8}{4}$$

Solve for x (complex solution)

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

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