Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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