Precalculus Examples

$\log_{9} (\frac{13 x^{2}}{y^{5}})$

Step 1

Rewrite $\log_{9} (\frac{13 x^{2}}{y^{5}})$ as $\log_{9} (13 x^{2}) - \log_{9} (y^{5})$ .

$\log_{9} (13 x^{2}) - \log_{9} (y^{5})$

Step 2

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

$\log_{9} (13 x^{2}) - (5 \log_{9} (y))$

Step 3

Multiply $5$ by $- 1$ .

$\log_{9} (13 x^{2}) - 5 \log_{9} (y)$

Step 4

Rewrite $\log_{9} (13 x^{2})$ as $\log_{9} (13) + \log_{9} (x^{2})$ .

$\log_{9} (13) + \log_{9} (x^{2}) - 5 \log_{9} (y)$

Step 5

Expand $\log_{9} (x^{2})$ by moving $2$ outside the logarithm.

$\log_{9} (13) + 2 \log_{9} (x) - 5 \log_{9} (y)$