Expand the Logarithmic Expression natural log of r/(6s)

$\ln (\frac{r}{6 s})$

Rewrite $\ln (\frac{r}{6 s})$ as $\ln (r) - \ln (6 s)$ .

$\ln (r) - \ln (6 s)$

Rewrite $\ln (6 s)$ as $\ln (6) + \ln (s)$ .

$\ln (r) - (\ln (6) + \ln (s))$

Simplify each term.

Rewrite $\ln (6)$ as $\ln (2 (3))$ .

$\ln (r) - (\ln (2 (3)) + \ln (s))$

Rewrite $\ln (2 (3))$ as $\ln (2) + \ln (3)$ .

$\ln (r) - (\ln (2) + \ln (3) + \ln (s))$

Apply the distributive property.

$\ln (r) - \ln (2) - \ln (3) - \ln (s)$