# How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_8 3?

Jul 17, 2015

I found: ${\log}_{8} \left(3\right) = \frac{\ln \left(3\right)}{\ln \left(8\right)} = 0.5283$
The change of base formula can be used to change the base of a log, say $b$, into another, say $c$, and can be written as:
${\log}_{b} a = {\log}_{c} \frac{a}{\log} _ c b$
Normally you choose a new base that should be "easier" to use. In this case I would choose $e$ that can be evaluated using a normal pocket calculator:
${\log}_{8} \left(3\right) = {\log}_{e} \frac{3}{{\log}_{e} \left(8\right)} = \frac{\ln \left(3\right)}{\ln \left(8\right)} = 0.5283$