Trigonometry Examples

$\log ({(\frac{u^{2}}{v})}^{3})$

Step 1

Expand $\log ({(\frac{u^{2}}{v})}^{3})$ by moving $3$ outside the logarithm.

$3 \log (\frac{u^{2}}{v})$

Step 2

Rewrite $\log (\frac{u^{2}}{v})$ as $\log (u^{2}) - \log (v)$ .

$3 (\log (u^{2}) - \log (v))$

Step 3

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

$3 (2 \log (u) - \log (v))$

Step 4

Apply the distributive property.

$3 (2 \log (u)) + 3 (- \log (v))$

Step 5

Multiply $2$ by $3$ .

$6 \log (u) + 3 (- \log (v))$

Step 6

Multiply $- 1$ by $3$ .

$6 \log (u) - 3 \log (v)$