Precalculus Examples

$\log (a^{6} x^{3} y z^{5})$

Step 1

Rewrite $\log (a^{6} x^{3} y z^{5})$ as $\log (a^{6} x^{3} y) + \log (z^{5})$ .

$\log (a^{6} x^{3} y) + \log (z^{5})$

Step 2

Rewrite $\log (a^{6} x^{3} y)$ as $\log (a^{6} x^{3}) + \log (y)$ .

$\log (a^{6} x^{3}) + \log (y) + \log (z^{5})$

Step 3

Rewrite $\log (a^{6} x^{3})$ as $\log (a^{6}) + \log (x^{3})$ .

$\log (a^{6}) + \log (x^{3}) + \log (y) + \log (z^{5})$

Step 4

Expand $\log (a^{6})$ by moving $6$ outside the logarithm.

$6 \log (a) + \log (x^{3}) + \log (y) + \log (z^{5})$

Step 5

Expand $\log (x^{3})$ by moving $3$ outside the logarithm.

$6 \log (a) + 3 \log (x) + \log (y) + \log (z^{5})$

Step 6

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

$6 \log (a) + 3 \log (x) + \log (y) + 5 \log (z)$