How do you use the Change of Base Formula and a calculator to evaluate #log_2 8#?

1 Answer
Gió
Oct 19, 2015

You should get #3#:

Explanation:

Actually using the definition of log you get:
#log_2(8)=x#
#2^x=8#
#2^x=2^3#
#x=3#
or:

The Change of Base Formula tells you that:
#log_ab=log_cb/log_ca# where #a# is the old and #c# is the new base.
We can choose #c=10# that gives you a log that can easily be evaluated using a pocket calculator getting:
#log_2(8)=log_10(8)/log_10(2)=3#

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