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

1 Answer
Dec 30, 2015

log_pi 14.2~~2.32

Explanation:

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))