Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Rewrite $\ln (3 y)$ as $\ln (3) + \ln (y)$ .

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

Step 5

Apply the distributive property.

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