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

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

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

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

Rewrite $\log_{4} (2 w^{4})$ as $\log_{4} (2) + \log_{4} (w^{4})$ .

$3 (\log_{4} (2) + \log_{4} (w^{4}))$

Expand $\log_{4} (w^{4})$ by moving $4$ outside the logarithm.

$3 (\log_{4} (2) + 4 \log_{4} (w))$

Logarithm base $4$ of $2$ is $\frac{1}{2}$ .

$3 (\frac{1}{2} + 4 \log_{4} (w))$

Apply the distributive property.

$3 (\frac{1}{2}) + 3 (4 \log_{4} (w))$

Combine $3$ and $\frac{1}{2}$ .

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

Multiply $4$ by $3$ .

$\frac{3}{2} + 12 \log_{4} (w)$