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

Question

2829 views around the world

You can reuse this answer
Creative Commons License

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

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