Solve 2^4=8^x

$$2 ^ { 4 } = 8 ^ { x }$$

Solve for x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Steps Using Definition of Logarithm

Calculate 2 to the power of 4 and get 16.

$$16=8^{x}$$

Swap sides so that all variable terms are on the left hand side.

$$8^{x}=16$$

Take the logarithm of both sides of the equation.

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

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

$$x\log(8)=\log(16)$$

Divide both sides by \log(8).

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

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

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

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(2)}+\frac{4}{3}$$

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