Precalculus Examples

$\log (a x^{2} y z^{5})$

Step 1

Rewrite $\log (a x^{2} y z^{5})$ as $\log (a x^{2} y) + \log (z^{5})$ .

$\log (a x^{2} y) + \log (z^{5})$

Step 2

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

$\log (a x^{2}) + \log (y) + \log (z^{5})$

Step 3

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

$\log (a) + \log (x^{2}) + \log (y) + \log (z^{5})$

Step 4

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

$\log (a) + 2 \log (x) + \log (y) + \log (z^{5})$

Step 5

Expand $\log (z^{5})$ by moving $5$ outside the logarithm.

$\log (a) + 2 \log (x) + \log (y) + 5 \log (z)$