Expand the Logarithmic Expression log base 6 of (8/5)^4

$\log_{6} ({(\frac{8}{5})}^{4})$

Expand $\log_{6} ({(\frac{8}{5})}^{4})$ by moving $4$ outside the logarithm.

$4 \log_{6} (\frac{8}{5})$

Rewrite $\log_{6} (\frac{8}{5})$ as $\log_{6} (8) - \log_{6} (5)$ .

$4 (\log_{6} (8) - \log_{6} (5))$

Simplify each term.

Rewrite $\log_{6} (8)$ as $\log_{6} (2^{3})$ .

$4 (\log_{6} (2^{3}) - \log_{6} (5))$

Expand $\log_{6} (2^{3})$ by moving $3$ outside the logarithm.

$4 (3 \log_{6} (2) - \log_{6} (5))$

Apply the distributive property.

$4 (3 \log_{6} (2)) + 4 (- \log_{6} (5))$

Multiply $3$ by $4$ .

$12 \log_{6} (2) + 4 (- \log_{6} (5))$

Multiply $- 1$ by $4$ .

$12 \log_{6} (2) - 4 \log_{6} (5)$