Expand the Logarithmic Expression natural log of m/8(p-9)

$\ln (\frac{m}{8} (p - 9))$

Rewrite $\ln (\frac{m}{8} (p - 9))$ as $\ln (\frac{m}{8}) + \ln (p - 9)$ .

$\ln (\frac{m}{8}) + \ln (p - 9)$

Rewrite $\ln (\frac{m}{8})$ as $\ln (m) - \ln (8)$ .

$\ln (m) - \ln (8) + \ln (p - 9)$

Rewrite $\ln (8)$ as $\ln (2^{3})$ .

$\ln (m) - \ln (2^{3}) + \ln (p - 9)$

Expand $\ln (2^{3})$ by moving $3$ outside the logarithm.

$\ln (m) - (3 \ln (2)) + \ln (p - 9)$

Multiply $3$ by $- 1$ .

$\ln (m) - 3 \ln (2) + \ln (p - 9)$