Solve 2^x-4=17

$$2 ^ { x - 4 } = 17$$

Solve for x

$$x=\log_{2}\left(17\right)+4\approx 8.087462841$$

Steps Using Definition of Logarithm

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

$$2^{x-4}=17$$

Take the logarithm of both sides of the equation.

$$\log(2^{x-4})=\log(17)$$

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

$$\left(x-4\right)\log(2)=\log(17)$$

Divide both sides by \log(2).

$$x-4=\frac{\log(17)}{\log(2)}$$

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

$$x-4=\log_{2}\left(17\right)$$

Add 4 to both sides of the equation.

$$x=\log_{2}\left(17\right)-\left(-4\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(2)}+\log_{2}\left(17\right)+4$$

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