Question

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

Answer 1

Algorithm is described below.

Explanation:

The Change of Base Formula states, that :

`log_a b=(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 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 "`MR`" 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.