Precalculus Examples

$\ln (\frac{3 x^{4}}{{(z y)}^{2}})$

Step 1

Rewrite $\ln (\frac{3 x^{4}}{{(z y)}^{2}})$ as $\ln (3 x^{4}) - \ln ({(z y)}^{2})$ .

$\ln (3 x^{4}) - \ln ({(z y)}^{2})$

Step 2

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

$\ln (3 x^{4}) - (2 \ln (z y))$

Step 3

Multiply $2$ by $- 1$ .

$\ln (3 x^{4}) - 2 \ln (z y)$

Step 4

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

$\ln (3) + \ln (x^{4}) - 2 \ln (z y)$

Step 5

Expand $\ln (x^{4})$ by moving $4$ outside the logarithm.

$\ln (3) + 4 \ln (x) - 2 \ln (z y)$

Step 6

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

$\ln (3) + 4 \ln (x) - 2 (\ln (z) + \ln (y))$

Step 7

Apply the distributive property.

$\ln (3) + 4 \ln (x) - 2 \ln (z) - 2 \ln (y)$