Expand the Logarithmic Expression natural log of (xy^2)^6

$\ln ({(x y^{2})}^{6})$

Expand $\ln ({(x y^{2})}^{6})$ by moving $6$ outside the logarithm.

$6 \ln (x y^{2})$

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

$6 (\ln (x) + \ln (y^{2}))$

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

$6 (\ln (x) + 2 \ln (y))$

Apply the distributive property.

$6 \ln (x) + 6 (2 \ln (y))$

Multiply $2$ by $6$ .

$6 \ln (x) + 12 \ln (y)$