Expand the Logarithmic Expression natural log of ((m^5)/(n^2))^3

$\ln ({(\frac{m^{5}}{n^{2}})}^{3})$

Expand $\ln ({(\frac{m^{5}}{n^{2}})}^{3})$ by moving $3$ outside the logarithm.

$3 \ln (\frac{m^{5}}{n^{2}})$

Rewrite $\ln (\frac{m^{5}}{n^{2}})$ as $\ln (m^{5}) - \ln (n^{2})$ .

$3 (\ln (m^{5}) - \ln (n^{2}))$

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

$3 (5 \ln (m) - \ln (n^{2}))$

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

$3 (5 \ln (m) - (2 \ln (n)))$

Multiply $2$ by $- 1$ .

$3 (5 \ln (m) - 2 \ln (n))$

Apply the distributive property.

$3 (5 \ln (m)) + 3 (- 2 \ln (n))$

Multiply $5$ by $3$ .

$15 \ln (m) + 3 (- 2 \ln (n))$

Multiply $- 2$ by $3$ .

$15 \ln (m) - 6 \ln (n)$