Expand the Logarithmic Expression natural log of 3/(5x^5y)

$\ln (\frac{3}{5 x^{5} y})$

Rewrite $\ln (\frac{3}{5 x^{5} y})$ as $\ln (3) - \ln (5 x^{5} y)$ .

$\ln (3) - \ln (5 x^{5} y)$

Rewrite $\ln (5 x^{5} y)$ as $\ln (5 x^{5}) + \ln (y)$ .

$\ln (3) - (\ln (5 x^{5}) + \ln (y))$

Rewrite $\ln (5 x^{5})$ as $\ln (5) + \ln (x^{5})$ .

$\ln (3) - (\ln (5) + \ln (x^{5}) + \ln (y))$

Expand $\ln (x^{5})$ by moving $5$ outside the logarithm.

$\ln (3) - (\ln (5) + 5 \ln (x) + \ln (y))$

Simplify each term.

Apply the distributive property.

$\ln (3) - \ln (5) - (5 \ln (x)) - \ln (y)$

Multiply $5$ by $- 1$ .

$\ln (3) - \ln (5) - 5 \ln (x) - \ln (y)$