Precalculus Examples

$\log (\frac{x^{4} z}{y^{9}})$

Step 1

Rewrite $\log (\frac{x^{4} z}{y^{9}})$ as $\log (x^{4} z) - \log (y^{9})$ .

$\log (x^{4} z) - \log (y^{9})$

Step 2

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

$\log (x^{4} z) - (9 \log (y))$

Step 3

Multiply $9$ by $- 1$ .

$\log (x^{4} z) - 9 \log (y)$

Step 4

Rewrite $\log (x^{4} z)$ as $\log (x^{4}) + \log (z)$ .

$\log (x^{4}) + \log (z) - 9 \log (y)$

Step 5

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

$4 \log (x) + \log (z) - 9 \log (y)$