Solve 256=16^x

$$256 = 16 ^ { x }$$

Solve for x

$$x=2$$

Steps Using Definition of Logarithm

Swap sides so that all variable terms are on the left hand side.

$$16^{x}=256$$

Take the logarithm of both sides of the equation.

$$\log(16^{x})=\log(256)$$

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

$$x\log(16)=\log(256)$$

Divide both sides by \log(16).

$$x=\frac{\log(256)}{\log(16)}$$

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

$$x=\log_{16}\left(256\right)$$

Solve for x (complex solution)

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

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