# How do you expand Ln( sqrt(a ^2 times b) /root4(b))?

Jun 15, 2016

Use the rule $\ln \left(\frac{a}{n}\right) = \ln a - \ln n$.

$= \ln \sqrt{{a}^{2} b} - \ln {b}^{\frac{1}{4}}$

$= \ln {\left({a}^{2} b\right)}^{\frac{1}{2}} - \ln {b}^{\frac{1}{4}}$

Use the rule $\log {a}^{n} = n \log$.

$= \frac{1}{2} \ln \left({a}^{2} b\right) - \frac{1}{4} \ln b$

You can expand using the rule $\ln \left(a \times b\right) = \ln a + \ln b$.

$= \frac{1}{2} \left(\ln {a}^{2} + \ln b\right) - \frac{1}{4} \ln b$

$= \frac{1}{2} \ln {a}^{2} + \frac{1}{2} \ln b - \frac{1}{4} \ln b$

It is possible to simplify further but that would involve compressing. I don't know what you want...

Hopefully this helps!