Expand the Logarithmic Expression natural log of 2/(3x^3y)

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

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

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

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

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

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

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

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

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

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $- 1$ .

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