Solve 2^x-2=8

$$2 ^ { x - 2 } = 8$$

Solve for x

$$x=5$$

Steps Using Definition of Logarithm

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

$$2^{x-2}=8$$

Take the logarithm of both sides of the equation.

$$\log(2^{x-2})=\log(8)$$

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

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

Divide both sides by \log(2).

$$x-2=\frac{\log(8)}{\log(2)}$$

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

$$x-2=\log_{2}\left(8\right)$$

Add 2 to both sides of the equation.

$$x=3-\left(-2\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(2)}+5$$

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