Solve 8^x-3=16

$$8 ^ { x - 3 } = 16$$

Solve for x

$$x = \frac{13}{3} = 4\frac{1}{3} \approx 4.333333333$$

Steps Using Definition of Logarithm

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

$$8^{x-3}=16$$

Take the logarithm of both sides of the equation.

$$\log(8^{x-3})=\log(16)$$

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

$$\left(x-3\right)\log(8)=\log(16)$$

Divide both sides by \log(8).

$$x-3=\frac{\log(16)}{\log(8)}$$

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

$$x-3=\log_{8}\left(16\right)$$

Add 3 to both sides of the equation.

$$x=\frac{4}{3}-\left(-3\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{3\ln(2)}+\frac{13}{3}$$

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