# How do you expand log (6/11)^5?

$5 \log 6 - 5 \log 11$
• $\log {\left(\frac{6}{11}\right)}^{5} = 5 \log \left(\frac{6}{11}\right)$ because $\log {a}^{b} = b \log a$
• $= 5 \left(\log 6 - \log 11\right)$ because $\log \left(\frac{a}{b}\right) = \log a - \log b$
• $= 5 \log 6 - 5 \log 11$ because $a \left(b - c\right) = a b - a c$