# How do you expand ln sqrt(x^3/y^2)?

Jul 26, 2016

$\frac{3}{2} \cdot \ln x - \ln y$

#### Explanation:

$\ln \sqrt{{x}^{3} / {y}^{2}}$ can be rewritten as

$\ln {\left({x}^{3} / {y}^{2}\right)}^{\frac{1}{2}}$

or $\ln \left({x}^{\frac{3}{2}} / {y}^{\frac{2}{2}}\right)$

using one of logarithm rules: $\ln \left(\frac{a}{b}\right) = \ln a - \ln b$

we have:

$\ln {x}^{\frac{3}{2}} - \ln {y}^{\frac{2}{2}}$

or $\ln {x}^{\frac{3}{2}} - \ln y$

another one of these rules state that: $\ln {a}^{b} = b \cdot \ln a$

then we have:

$\frac{3}{2} \cdot \ln x - \ln y$