How do you use the Change of Base Formula and a calculator to evaluate the logarithm #log_3 48#?

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Answer 1 · 2016-01-12T17:03:33

≈ 3.524 (3 decimal places)

#log_a x # may be converted to the base b by using the following formula :

# log_b x/log_b a # (x > 1 )

In this case write # log_3 48 = log_10 48 /log_10 3 #

Other bases , apart from base 10 may be used. Base 10 is convenient as it can be evaluated on a calculator ( as of course can ln)

When using base 10 it is usual for it to be written without the 10.

#rArr log_10 48/log_10 3 = log 48/log 3 #

using the log key on a calculator (this is to base 10 )

#rArr log48/log3 = 1.68124/0.47712 ≈3.524#