Precalculus Examples

$\log ({(\frac{p^{4}}{q^{7}})}^{2})$

Step 1

Expand $\log ({(\frac{p^{4}}{q^{7}})}^{2})$ by moving $2$ outside the logarithm.

$2 \log (\frac{p^{4}}{q^{7}})$

Step 2

Rewrite $\log (\frac{p^{4}}{q^{7}})$ as $\log (p^{4}) - \log (q^{7})$ .

$2 (\log (p^{4}) - \log (q^{7}))$

Step 3

Expand $\log (p^{4})$ by moving $4$ outside the logarithm.

$2 (4 \log (p) - \log (q^{7}))$

Step 4

Expand $\log (q^{7})$ by moving $7$ outside the logarithm.

$2 (4 \log (p) - (7 \log (q)))$

Step 5

Multiply $7$ by $- 1$ .

$2 (4 \log (p) - 7 \log (q))$

Step 6

Apply the distributive property.

$2 (4 \log (p)) + 2 (- 7 \log (q))$

Step 7

Multiply $4$ by $2$ .

$8 \log (p) + 2 (- 7 \log (q))$

Step 8

Multiply $- 7$ by $2$ .

$8 \log (p) - 14 \log (q)$