Precalculus Examples

$\log (\frac{x^{6} y^{7}}{z^{9}})$

Step 1

Rewrite $\log (\frac{x^{6} y^{7}}{z^{9}})$ as $\log (x^{6} y^{7}) - \log (z^{9})$ .

$\log (x^{6} y^{7}) - \log (z^{9})$

Step 2

Expand $\log (z^{9})$ by moving $9$ outside the logarithm.

$\log (x^{6} y^{7}) - (9 \log (z))$

Step 3

Multiply $9$ by $- 1$ .

$\log (x^{6} y^{7}) - 9 \log (z)$

Step 4

Rewrite $\log (x^{6} y^{7})$ as $\log (x^{6}) + \log (y^{7})$ .

$\log (x^{6}) + \log (y^{7}) - 9 \log (z)$

Step 5

Expand $\log (x^{6})$ by moving $6$ outside the logarithm.

$6 \log (x) + \log (y^{7}) - 9 \log (z)$

Step 6

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

$6 \log (x) + 7 \log (y) - 9 \log (z)$