Evaluate log base 4 of 4^(2/3)

$\log_{4} (4^{\frac{2}{3}})$

Use logarithm rules to move $\frac{2}{3}$ out of the exponent.

$\frac{2}{3} \log_{4} (4)$

Logarithm base $4$ of $4$ is $1$ .

$\frac{2}{3} \cdot 1$

Multiply $\frac{2}{3}$ by $1$ .

$\frac{2}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$