Precalculus Examples

$\log (\frac{2 x^{3}}{y z})$

Step 1

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

$\log (2 x^{3}) - \log (y z)$

Step 2

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

$\log (2) + \log (x^{3}) - \log (y z)$

Step 3

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

$\log (2) + 3 \log (x) - \log (y z)$

Step 4

Rewrite $\log (y z)$ as $\log (y) + \log (z)$ .

$\log (2) + 3 \log (x) - (\log (y) + \log (z))$

Step 5

Apply the distributive property.

$\log (2) + 3 \log (x) - \log (y) - \log (z)$