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Just What is a Logarithm, Anyway?

Before we talk about logarithms, let's think a little bit about graphing.

Grade Level: Middle School (6-8)
Curriculum Topic Benchmarks: M2.3.2, M2.3.4, M2.3.5, M2.3.7, M4.3.19, M8.3.1, M8.3.2, M8.3.3, M8.3.4, M8.3.7, M8.3.12
Subject Keywords: Logarithm, Log, Graph, Decibel, Space Shuttle, Sound, Vibration, Richter scale, Earthquake

Author(s): Kim Aaron
PUMAS ID: 06_01_97_1
Date Received: 1997-06-01
Date Revised: 1997-10-30
Date Accepted: 1997-10-30

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Comment by Rex Boggs on February 5, 1999
"Very readable article. But I take objection to the statement, "The logarithm of a number is how many times you have to multiply 10 by itself to get that number." The example was:

10 000 = 10 x 10 x 10 x 10

Here 10 was multiplied by itself three times, not four. Just count the multiplication signs! A better statement is "The logarithm of a number is how many factors of 10 are multiplied together to get that number"."

Comment by Kim Aaron on October 9, 2011
"I wrote the paper and I agree with Rex Boggs' comment. I don't intend to rewrite it, but I have actually thought about this comment many times over the intervening years. If he ever comes back here, I hope he will be glad that his comment made me do a lot of thinking. He may have thought I never saw his comment or that I didn't care. Quite the opposite. I don't know why I never wrote a reply before now, though. In my mind, I refer this this as the "N-1 problem". Sometimes, we count from 1 and sometimes we count from 0. Computer programmers ofter count from 0.

I've even toyed with the idea of writing a PUMAS paper called "The N-1 Problem." Some of the reasons I never rewrote the paper is that I though the wording would get pedantic and I couldn't think of an easy way to express it. I also figured that anyone reading the paper would see Rex's comment and they would understand what I meant as a result and could deal with it. Thanks for the comment, Rex. I really do appreciate it."

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