Expand the Logarithmic Expression log base 2 of (a^5b^2)^3

$\log_{2} ({(a^{5} b^{2})}^{3})$

Expand $\log_{2} ({(a^{5} b^{2})}^{3})$ by moving $3$ outside the logarithm.

$3 \log_{2} (a^{5} b^{2})$

Rewrite $\log_{2} (a^{5} b^{2})$ as $\log_{2} (a^{5}) + \log_{2} (b^{2})$ .

$3 (\log_{2} (a^{5}) + \log_{2} (b^{2}))$

Expand $\log_{2} (a^{5})$ by moving $5$ outside the logarithm.

$3 (5 \log_{2} (a) + \log_{2} (b^{2}))$

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

$3 (5 \log_{2} (a) + 2 \log_{2} (b))$

Apply the distributive property.

$3 (5 \log_{2} (a)) + 3 (2 \log_{2} (b))$

Multiply $5$ by $3$ .

$15 \log_{2} (a) + 3 (2 \log_{2} (b))$

Multiply $2$ by $3$ .

$15 \log_{2} (a) + 6 \log_{2} (b)$