Expand the Logarithmic Expression natural log of 20x^3y^2

$\ln (20 x^{3} y^{2})$

Rewrite $\ln (20 x^{3} y^{2})$ as $\ln (20 x^{3}) + \ln (y^{2})$ .

$\ln (20 x^{3}) + \ln (y^{2})$

Rewrite $\ln (20 x^{3})$ as $\ln (20) + \ln (x^{3})$ .

$\ln (20) + \ln (x^{3}) + \ln (y^{2})$

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

$\ln (20) + 3 \ln (x) + \ln (y^{2})$

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

$\ln (20) + 3 \ln (x) + 2 \ln (y)$

Simplify each term.

Rewrite $\ln (20)$ as $\ln (2^{2} \cdot 5)$ .

$\ln (2^{2} \cdot 5) + 3 \ln (x) + 2 \ln (y)$

Rewrite $\ln (2^{2} \cdot 5)$ as $\ln (2^{2}) + \ln (5)$ .

$\ln (2^{2}) + \ln (5) + 3 \ln (x) + 2 \ln (y)$

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

$2 \ln (2) + \ln (5) + 3 \ln (x) + 2 \ln (y)$