Precalculus Examples

$\log ({(x y^{5})}^{2})$

Step 1

Expand $\log ({(x y^{5})}^{2})$ by moving $2$ outside the logarithm.

$2 \log (x y^{5})$

Step 2

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

$2 (\log (x) + \log (y^{5}))$

Step 3

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

$2 (\log (x) + 5 \log (y))$

Step 4

Apply the distributive property.

$2 \log (x) + 2 (5 \log (y))$

Step 5

Multiply $5$ by $2$ .

$2 \log (x) + 10 \log (y)$