How do you use the Change of Base Formula and a calculator to evaluate the logarithm #log 4^20#?

1 Answer
Jim H
Aug 15, 2015

#log_4 20 = ln20/ln4 = log20/log4 ~~ 2.1610 #

Explanation:

There is a good possibility that the intended question is to find #log_4 20# rather than the apparent question of find #log 4^20#

In any case the change of base formula says (in its general form) that

For a, b, x positive,

#log_b x = log_a x/(log_a b)#

Because calculators tend to have built-in functions for base 10 logs, #log_10# (often written #log#) and/or natural logs #ln#, it is not unusual to see the change of base formula given as:

For b, x positive,

#log_b x = log x/(log b)" "# or #" "log_b x = ln x/(ln b)#

The sequence of button to press depends on the calculator you are using.

On the calculator that is included in windows (scientific view)

press: 20 "ln" / 4 "ln" =

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