How do you use the Change of Base Formula and a calculator to evaluate the logarithm #log_4 24#?

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Answer 1 · 2018-06-12T02:35:36

Below

The change of base formula is given by: #log_ab = log_10b/log_10a#

Looking at #log_4 24#, we can tell that a=4 and b=24.

#log_4 24 = log_10 24/log_10 4 = 2.292#

Answer 2 · 2018-06-12T07:46:29

#y=2.29248#(5 dps)

from first principles

#y=log_4 24#

#=>4^y=24#

take logs to both sides ( we will use base 10)

#log4^y=log24#

#ylog4=log24#

#y=log24/log4#

#y=2.29248125#

note: some calculators now have a function that can evaluates logarithms in any base