Expand the Logarithmic Expression natural log of 4x^2y^5

$\ln (4 x^{2} y^{5})$

Rewrite $\ln (4 x^{2} y^{5})$ as $\ln (4 x^{2}) + \ln (y^{5})$ .

$\ln (4 x^{2}) + \ln (y^{5})$

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

$\ln (4) + \ln (x^{2}) + \ln (y^{5})$

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

$\ln (4) + 2 \ln (x) + \ln (y^{5})$

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

$\ln (4) + 2 \ln (x) + 5 \ln (y)$

Simplify each term.

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

$\ln (2^{2}) + 2 \ln (x) + 5 \ln (y)$

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

$2 \ln (2) + 2 \ln (x) + 5 \ln (y)$