Solve 8^x=128

$${ 8 }^{ x } =128$$

Solve for x

$$x = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

Steps Using Definition of Logarithm

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

$$8^{x}=128$$

Take the logarithm of both sides of the equation.

$$\log(8^{x})=\log(128)$$

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

$$x\log(8)=\log(128)$$

Divide both sides by \log(8).

$$x=\frac{\log(128)}{\log(8)}$$

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

$$x=\log_{8}\left(128\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(2)}+\frac{7}{3}$$

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