Base of Common LogarithmsDate: 05/23/2000 at 20:57:42 From: Courtney Shannon Subject: Logarithms and base ten Why is the base of common logarithms 10? Is it easier to work with, or is there a mathematical explanation? Date: 05/24/2000 at 12:48:28 From: Doctor Peterson Subject: Re: Logarithms and base ten Hi, Courtney. When logarithms were used to just make calculations easier, it was natural to use base 10 logs because they fit well with base 10 numbers. It's easy to find the log of 10, 100, 1000, and so on; and if you have a table of logs of numbers from 1 to 10, you can use nothing more than addition to use it for larger or smaller numbers: log(5) = 0.69897 log(50) = log(10*5) = log(10) + log(5) = 1 + 0.69897 = 1.69897 So common logarithms make it easier to make and use a table. That's really all they're good for - except to determine how many digits a number has (in base 10, of course). Mathematically, common logs are NOT particularly "natural"; we usually work with "natural logs" (base e), which arise naturally in calculus, or else with whatever log fits the work we are doing. Base 2 logs are useful in working with binary numbers, for example. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/