Precalculus Examples

$\log_{5} (\frac{u^{3}}{v^{2}})$

Step 1

Rewrite $\log_{5} (\frac{u^{3}}{v^{2}})$ as $\log_{5} (u^{3}) - \log_{5} (v^{2})$ .

$\log_{5} (u^{3}) - \log_{5} (v^{2})$

Step 2

Expand $\log_{5} (u^{3})$ by moving $3$ outside the logarithm.

$3 \log_{5} (u) - \log_{5} (v^{2})$

Step 3

Expand $\log_{5} (v^{2})$ by moving $2$ outside the logarithm.

$3 \log_{5} (u) - (2 \log_{5} (v))$

Step 4

Multiply $2$ by $- 1$ .

$3 \log_{5} (u) - 2 \log_{5} (v)$