# How do you expand  ln(sqrt13.5)?

Apr 7, 2017

#### Explanation:

Write the square root as the $\frac{1}{2}$ power:

$\ln \left({\left(13.5\right)}^{\frac{1}{2}}\right)$

Write $13.5$ as $\frac{27}{2}$:

$\ln \left({\left(\frac{27}{2}\right)}^{\frac{1}{2}}\right)$

Use the property $\ln \left({a}^{c}\right) = \left(c\right) \ln \left(a\right)$:

$\frac{1}{2} \left(\ln \left(\frac{27}{2}\right)\right)$

Use the property $\ln \left(\frac{a}{c}\right) = \ln \left(a\right) - \ln \left(c\right)$

$\frac{1}{2} \left(\ln \left(27\right) - \ln \left(2\right)\right)$

You can distribute the $\frac{1}{2}$, if you like but I think this is fine.