Precalculus Examples

$\log (\frac{5 y^{3}}{x^{5}})$

Step 1

Rewrite $\log (\frac{5 y^{3}}{x^{5}})$ as $\log (5 y^{3}) - \log (x^{5})$ .

$\log (5 y^{3}) - \log (x^{5})$

Step 2

Expand $\log (x^{5})$ by moving $5$ outside the logarithm.

$\log (5 y^{3}) - (5 \log (x))$

Step 3

Multiply $5$ by $- 1$ .

$\log (5 y^{3}) - 5 \log (x)$

Step 4

Rewrite $\log (5 y^{3})$ as $\log (5) + \log (y^{3})$ .

$\log (5) + \log (y^{3}) - 5 \log (x)$

Step 5

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

$\log (5) + 3 \log (y) - 5 \log (x)$