Precalculus Examples

$\log_{a} (\frac{3 x^{2} y}{z^{4}})$

Step 1

Rewrite $\log_{a} (\frac{3 x^{2} y}{z^{4}})$ as $\log_{a} (3 x^{2} y) - \log_{a} (z^{4})$ .

$\log_{a} (3 x^{2} y) - \log_{a} (z^{4})$

Step 2

Expand $\log_{a} (z^{4})$ by moving $4$ outside the logarithm.

$\log_{a} (3 x^{2} y) - (4 \log_{a} (z))$

Step 3

Multiply $4$ by $- 1$ .

$\log_{a} (3 x^{2} y) - 4 \log_{a} (z)$

Step 4

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

$\log_{a} (3 x^{2}) + \log_{a} (y) - 4 \log_{a} (z)$

Step 5

Rewrite $\log_{a} (3 x^{2})$ as $\log_{a} (3) + \log_{a} (x^{2})$ .

$\log_{a} (3) + \log_{a} (x^{2}) + \log_{a} (y) - 4 \log_{a} (z)$

Step 6

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

$\log_{a} (3) + 2 \log_{a} (x) + \log_{a} (y) - 4 \log_{a} (z)$