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

1 Answer
Daniel L.
Sep 14, 2015

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.

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