# How do you evaluate log_(1/2) (9/4)?

Oct 6, 2015

$\log \frac{\frac{9}{4}}{\log} \left(\frac{1}{2}\right)$

#### Explanation:

Let $x = {\log}_{\frac{1}{2}} \left(\frac{9}{4}\right)$

Then it is ${\left(\frac{1}{2}\right)}^{x} = \frac{9}{4}$

Taking log on both sides x=$\log \frac{\frac{9}{4}}{\log} \left(\frac{1}{2}\right)$. This can be evaluated in decimals if required.