Precalculus Examples

$\log (\frac{x^{3} y^{4}}{z^{6}})$

Step 1

Rewrite $\log (\frac{x^{3} y^{4}}{z^{6}})$ as $\log (x^{3} y^{4}) - \log (z^{6})$ .

$\log (x^{3} y^{4}) - \log (z^{6})$

Step 2

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

$\log (x^{3} y^{4}) - (6 \log (z))$

Step 3

Multiply $6$ by $- 1$ .

$\log (x^{3} y^{4}) - 6 \log (z)$

Step 4

Rewrite $\log (x^{3} y^{4})$ as $\log (x^{3}) + \log (y^{4})$ .

$\log (x^{3}) + \log (y^{4}) - 6 \log (z)$

Step 5

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

$3 \log (x) + \log (y^{4}) - 6 \log (z)$

Step 6

Expand $\log (y^{4})$ by moving $4$ outside the logarithm.

$3 \log (x) + 4 \log (y) - 6 \log (z)$