# How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_9 2.15?

Sep 16, 2015

I found: $0.3483$

#### Explanation:

The Change of Base Formula allows you to write:

${\log}_{a} b = \frac{{\log}_{c} b}{{\log}_{c} a}$
and change your base from $a$ to the new base $c$.

We can choose, as new base, $e$ and use natural logs, $\ln$, that can be evaluated using a pocket calculator and get:

${\log}_{9} \left(2.15\right) = \frac{\ln 2.15}{\ln 9} = 0.3483$