# How do you calculate log _(1/2) (9/4)?

Aug 31, 2016

${\log}_{\frac{1}{2}} \left(\frac{9}{4}\right) = - 1.17$

#### Explanation:

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

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

$\frac{1}{2} ^ x = \frac{9}{4}$ or

${2}^{x} = \frac{4}{9}$ or

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

= ${\log}_{2} 4 - {\log}_{2} 9$

= $2 - \log \frac{9}{\log} 2$

= $2 - \frac{0.9542}{0.3010}$

= $2 - 3.17 = - 1.17$