# How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_3 21.8?

Sep 14, 2015

Algorithm is described below.

#### Explanation:

The Change of Base Formula states, that :

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

So you can change logarythm to any base convinient. Calculators usually have 2 logarythms: decimal (base 10) and natural (base $e$), so you can calculate ${\log}_{3} 21.8$ as:

${\log}_{3} 21.8 = {\log}_{10} \frac{21.8}{\log} _ 10 3$

To calculate it on a calculator you should:

1) Press 3 and "$\log$" to count ${\log}_{10} 3$
2) Press "$M +$" to put the result in memory.
3) Press $21.3$, "$\log$".
4) Press "/"
5) Press "$M R$" to recall the result stored in memory in 2)
6) Press "=" to get final result.

Note: I described the algorithm using ${\log}_{10}$ but you can also use $\ln$ instead.