Precalculus Examples

$\log (\frac{x^{2} y}{z^{3}})$

Step 1

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

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

Step 2

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

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

Step 3

Multiply $3$ by $- 1$ .

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

Step 4

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

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

Step 5

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

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