# How do you use change of base to simplify log_7 83?

Feb 13, 2015

You use the fact that:
${\log}_{a} M = \ln \frac{M}{\ln} \left(a\right)$
${\log}_{7} \left(83\right) = \ln \frac{83}{\ln} \left(7\right) = 2.271$
${7}^{2.271} = 83.026 . . \approx 83$
(I use $\ln$, the natural log, but you can use the other log that your calculator uses, the one in base 10, the result is the same, try it)