How do you calculate #log_6 5# with a calculator?

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Answer 1 · 2016-08-12T22:49:58

#log_6 5 = log 5 / log 6 ~~ 0.8982444#

Use the change of base formula:

#log_a b = (log_c b) / (log_c a)#

So you can use natural or common logs:

#log_6 5 = ln 5 / ln 6#

#log_6 5 = log 5 / log 6#

In fact, if you know #log 2 ~~ 0.30103# and #log 3 ~~ 0.47712# then you can get a reasonable approximation with basic arithmetic operations:

#log_6 5 = log 5 / log 6 = (log 10 - log 2) / (log 2 + log 3)#

#~~ (1-0.30103)/(0.30103+0.47712) = 0.69897/0.77815 ~~ 0.89825#

Actually the true value is closer to #0.8982444#