# How do you find the value of log_(1/2) 15 using the change of base formula?

Feb 3, 2017

${\log}_{\frac{1}{2}} 15 = - 3.9073$

#### Explanation:

${\log}_{a} b = \log \frac{b}{\log} a$

Hence, ${\log}_{\frac{1}{2}} 15$

= $\log \frac{15}{\log} \left(\frac{1}{2}\right)$

= $\log \frac{15}{\log 1 - \log 2}$

= $\log \frac{15}{0 - \log 2}$

= $\frac{1.1761}{- 0.3010} = - 3.9073$