Precalculus Examples

$\log_{2} (\frac{a^{3}}{b^{2}})$

Step 1

Rewrite $\log_{2} (\frac{a^{3}}{b^{2}})$ as $\log_{2} (a^{3}) - \log_{2} (b^{2})$ .

$\log_{2} (a^{3}) - \log_{2} (b^{2})$

Step 2

Expand $\log_{2} (a^{3})$ by moving $3$ outside the logarithm.

$3 \log_{2} (a) - \log_{2} (b^{2})$

Step 3

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

$3 \log_{2} (a) - (2 \log_{2} (b))$

Step 4

Multiply $2$ by $- 1$ .

$3 \log_{2} (a) - 2 \log_{2} (b)$