Logarithms in Bases Other Than 10Date: 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 |
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