Logarithms in Bases Other Than 10

Date: 03/28/98 at 08:50:24
From: Gavin Tweedie
Subject: Logarithms in a base other than 10

I'm curious as to what methods are available for solving logarithms 
in a base other than 10. We are constantly told that we have to 
convert the bases manually, which is a waste when we all have graphic 
calculators. I think there must be a way it can be done! I have 
checked the manual for my calculator (Casio CFX 9850G) but it only 
mentions log to base 10 and natural logarithms. Is there any formula 
that can be used in association with the log function or any way of 
converting the bases on the calculator?

Thanks.
Gavin Tweedie

Date: 04/01/98 at 22:51:53
From: Doctor Barrus
Subject: Re: Logarithms in a base other than 10

Hi, Gavin!

I'm not sure what you mean by converting manually, but here's the 
method I use to convert logarithms of base a to base b:

(I'll use the notation log[a]x to mean the logarithm of x with base a. 
For example, log[2]8 = 3.)

To convert from one base to another, this is the rule:

                log[a]x
     log[b]x = ---------
                log[a]b

For example, to convert from base 10 to base 2, we would say:

                log[10]x
     log[2]x = ----------
                log[10]2

This is a useful formula. Also, as you can see, if you want to find 
the log of a number x in base b, all you have to do is take the log 
of x (in either base 10 or e) and divide by the log of b (in base 10
or e - make sure you use the same base for both x and b). In other 
words, each time you can just take the logarithm your calculator can 
do and divide it by the log of the desired base. If you have a 
programming calculator and know how to program it, you could write a 
program to do this for you. Check your user's manual.

Good luck!

-Doctor Barrus,  The Math Forum
Check out our web site! http://mathforum.org/dr.math/   

Date: 04/02/98 at 01:44:16
From: Gavin Tweedie
Subject: Re: Logarithms in a base other than 10

Thanks a lot,

Gavin Tweedie