Precalculus Examples

$\log ({(x^{2} \cdot y^{- 3})}^{2})$

Step 1

Expand $\log ({(x^{2} \cdot y^{- 3})}^{2})$ by moving $2$ outside the logarithm.

$2 \log (x^{2} \cdot y^{- 3})$

Step 2

Rewrite $\log (x^{2} \cdot y^{- 3})$ as $\log (x^{2}) + \log (y^{- 3})$ .

$2 (\log (x^{2}) + \log (y^{- 3}))$

Step 3

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

$2 (2 \log (x) + \log (y^{- 3}))$

Step 4

Expand $\log (y^{- 3})$ by moving $- 3$ outside the logarithm.

$2 (2 \log (x) - 3 \log (y))$

Step 5

Apply the distributive property.

$2 (2 \log (x)) + 2 (- 3 \log (y))$

Step 6

Multiply $2$ by $2$ .

$4 \log (x) + 2 (- 3 \log (y))$

Step 7

Multiply $- 3$ by $2$ .

$4 \log (x) - 6 \log (y)$