Solve 8^x=4

$${ 8 }^{ x } =4$$

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps Using Definition of Logarithm

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

$$8^{x}=4$$

Take the logarithm of both sides of the equation.

$$\log(8^{x})=\log(4)$$

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

$$x\log(8)=\log(4)$$

Divide both sides by \log(8).

$$x=\frac{\log(4)}{\log(8)}$$

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

$$x=\log_{8}\left(4\right)$$

Solve for x (complex solution)

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

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