Calculus Examples

$\log_{9} (\frac{x y^{3}}{z^{2}})$

Step 1

Rewrite $\log_{9} (\frac{x y^{3}}{z^{2}})$ as $\log_{9} (x y^{3}) - \log_{9} (z^{2})$ .

$\log_{9} (x y^{3}) - \log_{9} (z^{2})$

Step 2

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

$\log_{9} (x y^{3}) - (2 \log_{9} (z))$

Step 3

Multiply $2$ by $- 1$ .

$\log_{9} (x y^{3}) - 2 \log_{9} (z)$

Step 4

Rewrite $\log_{9} (x y^{3})$ as $\log_{9} (x) + \log_{9} (y^{3})$ .

$\log_{9} (x) + \log_{9} (y^{3}) - 2 \log_{9} (z)$

Step 5

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

$\log_{9} (x) + 3 \log_{9} (y) - 2 \log_{9} (z)$