Expand the Logarithmic Expression log of (6/11)^5

$\log ({(\frac{6}{11})}^{5})$

Step 1

Expand $\log ({(\frac{6}{11})}^{5})$ by moving $5$ outside the logarithm.

$5 \log (\frac{6}{11})$

Step 2

Rewrite $\log (\frac{6}{11})$ as $\log (6) - \log (11)$ .

$5 (\log (6) - \log (11))$

Step 3

Simplify each term.

Rewrite $\log (6)$ as $\log (2 (3))$ .

$5 (\log (2 (3)) - \log (11))$

Rewrite $\log (2 (3))$ as $\log (2) + \log (3)$ .

$5 (\log (2) + \log (3) - \log (11))$

Step 4

Apply the distributive property.

$5 \log (2) + 5 \log (3) + 5 (- \log (11))$

Step 5

Multiply $- 1$ by $5$ .

$5 \log (2) + 5 \log (3) - 5 \log (11)$