Expand the Logarithmic Expression natural log of (4m^5)/p

$\ln (\frac{4 m^{5}}{p})$

Rewrite $\ln (\frac{4 m^{5}}{p})$ as $\ln (4 m^{5}) - \ln (p)$ .

$\ln (4 m^{5}) - \ln (p)$

Rewrite $\ln (4 m^{5})$ as $\ln (4) + \ln (m^{5})$ .

$\ln (4) + \ln (m^{5}) - \ln (p)$

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

$\ln (4) + 5 \ln (m) - \ln (p)$

Simplify each term.

Rewrite $\ln (4)$ as $\ln (2^{2})$ .

$\ln (2^{2}) + 5 \ln (m) - \ln (p)$

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

$2 \ln (2) + 5 \ln (m) - \ln (p)$