How do you use the Change of Base Formula and a calculator to evaluate the logarithm #log_pi 14.2#?

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Answer 1 · 2015-12-30T19:05:45

#log_pi 14.2~~2.32#

To calculate #log_pi 14.2#, use any logarithm available on the calculator:

#log_10 14.2 ~~ 1.15#

Then divide the result by the logarithm of the number you wish to use as your base:

#log_10 pi ~~ 0.497#

#1.15/0.497 ~~ 2.32#

Simplified into a single expression:

#log_10 14.2/log_10 pi ~~ 2.32#

(Note how both logarithms above use the same base. The Change of Base formula will not yield the correct result, otherwise.)

Another common base is base #e#, or the natural logarithm (written #ln#).

This would be input into a calculator as:

#(ln(14.2))/(ln(pi))#