Expand the Logarithmic Expression log base 7 of (xy^5)^5

$\log_{7} ({(x y^{5})}^{5})$

Step 1

Expand $\log_{7} ({(x y^{5})}^{5})$ by moving $5$ outside the logarithm.

$5 \log_{7} (x y^{5})$

Step 2

Rewrite $\log_{7} (x y^{5})$ as $\log_{7} (x) + \log_{7} (y^{5})$ .

$5 (\log_{7} (x) + \log_{7} (y^{5}))$

Step 3

Expand $\log_{7} (y^{5})$ by moving $5$ outside the logarithm.

$5 (\log_{7} (x) + 5 \log_{7} (y))$

Step 4

Apply the distributive property.

$5 \log_{7} (x) + 5 (5 \log_{7} (y))$

Step 5

Multiply $5$ by $5$ .

$5 \log_{7} (x) + 25 \log_{7} (y)$