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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