Precalculus Examples

$\frac{\log_{9} ({(a^{3} b^{5})}^{3})}{c}$

Step 1

Expand $\log_{9} ({(a^{3} b^{5})}^{3})$ by moving $3$ outside the logarithm.

$\frac{3 \log_{9} (a^{3} b^{5})}{c}$

Step 2

Rewrite $\log_{9} (a^{3} b^{5})$ as $\log_{9} (a^{3}) + \log_{9} (b^{5})$ .

$\frac{3 (\log_{9} (a^{3}) + \log_{9} (b^{5}))}{c}$

Step 3

Expand $\log_{9} (a^{3})$ by moving $3$ outside the logarithm.

$\frac{3 (3 \log_{9} (a) + \log_{9} (b^{5}))}{c}$

Step 4

Expand $\log_{9} (b^{5})$ by moving $5$ outside the logarithm.

$\frac{3 (3 \log_{9} (a) + 5 \log_{9} (b))}{c}$