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

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify each term.

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

$6 (\log (2 (3)) - \log (5))$

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

$6 (\log (2) + \log (3) - \log (5))$

Step 4

Apply the distributive property.

$6 \log (2) + 6 \log (3) + 6 (- \log (5))$

Step 5

Multiply $- 1$ by $6$ .

$6 \log (2) + 6 \log (3) - 6 \log (5)$