Expand the Logarithmic Expression log base 2 of ((2^3)/13)^4

$\log_{2} ({(\frac{2^{3}}{13})}^{4})$

Expand $\log_{2} ({(\frac{2^{3}}{13})}^{4})$ by moving $4$ outside the logarithm.

$4 \log_{2} (\frac{2^{3}}{13})$

Raise $2$ to the power of $3$ .

$4 \log_{2} (\frac{8}{13})$

Rewrite $\log_{2} (\frac{8}{13})$ as $\log_{2} (8) - \log_{2} (13)$ .

$4 (\log_{2} (8) - \log_{2} (13))$

Logarithm base $2$ of $8$ is $3$ .

$4 (3 - \log_{2} (13))$

Apply the distributive property.

$4 \cdot 3 + 4 (- \log_{2} (13))$

Multiply $4$ by $3$ .

$12 + 4 (- \log_{2} (13))$

Multiply $- 1$ by $4$ .

$12 - 4 \log_{2} (13)$