# How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_(1/2) 15?

I found: $- 3.9$
${\log}_{a} b = {\log}_{c} \frac{b}{\log} _ c a$ so that basically you changed the old base $a$ into the new one $c$.
In our case we can choose, as new base, the number $e$ that gives us the natural log, $\ln$, that it is possible to find with a pocket calculator. So:
$\log \left(\frac{1}{2}\right) 15 = \ln \frac{15}{\ln} \left(\frac{1}{2}\right) = - 3.9$