Precalculus Examples

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

Step 1

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

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

Step 2

Rewrite $\log (x^{2} y^{3})$ as $\log (x^{2}) + \log (y^{3})$ .

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

Step 3

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

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

Step 4

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

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

Step 5

Rewrite $\log (z w)$ as $\log (z) + \log (w)$ .

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

Step 6

Apply the distributive property.

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