Solve (2)^x+2=256

$$( 2 ) ^ { x + 2 } = 256$$

Solve for x

$$x=6$$

Steps Using Definition of Logarithm

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

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

Take the logarithm of both sides of the equation.

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

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

$$\left(x+2\right)\log(2)=\log(256)$$

Divide both sides by \log(2).

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

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

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

Subtract 2 from both sides of the equation.

$$x=8-2$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(2)}+6$$

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