Solve (8^1/3)^2=4^x

$$( 8 ^ { 1 / 3 } ) ^ { 2 } = 4 ^ { x }$$

Solve for x

$$x=1$$

Steps Using Definition of Logarithm

To raise a power to another power, multiply the exponents. Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$8^{\frac{2}{3}}=4^{x}$$

Calculate 8 to the power of \frac{2}{3} and get 4.

$$4=4^{x}$$

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

$$4^{x}=4$$

Take the logarithm of both sides of the equation.

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

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

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

Divide both sides by \log(4).

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

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

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

Solve for x (complex solution)

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

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