Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Multiply $3$ by $- 1$ .

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

Step 4

Rewrite $\log_{a} (2 x y^{2})$ as $\log_{a} (2 x) + \log_{a} (y^{2})$ .

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

Step 5

Rewrite $\log_{a} (2 x)$ as $\log_{a} (2) + \log_{a} (x)$ .

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

Step 6

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

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