A math book by Dan Umbarger on solving logarithms
Explaining Logarithms
A Progression Of Ideas Illuminating An Important Mathematical Concept

Math Teacher | Philosophy Driving The Text Of This Math Book

Philosophy Driving The Text

For over 350 years, from the early 1600s until the widespread availability of calculators in the 1970s, most of the mathematics done by scientists, engineers, and astronomers was assisted by logarithms. The logarithmic technique was developed to aid in the drudgery of simplifying long and tedious arithmetic expressions. Logarithms worked by reducing arithmetic expressions of one level of difficulty to a lesser level of difficulty. Scientific calculators have made much of the pre-1970 Precalculus curriculum obsolete. But the use of calculators has also come with a price. The instruction of logarithms today is much, much more condensed and abstract than it used to be. As a result, many of today’s students do not achieve the same level of understanding and “internalization” of logarithmic concepts and ideas. Many of them do not understand the “magic” formulas they are taught and asked to manipulate.

The website The Math Forum, “Ask Dr. Math,” has the following request for help:

“I understand what logs are … but I don’t understand why they are what they are. Please help me.”

This is a plea for help from a student who, at the time of his plea, was enrolled in a calculus class!

Explaining Logarithms, A Progression of Ideas Illuminating an Important Mathematical Concept, does not advocate a return to the precalculator “good old days.” The author lived through them. They were not so good!! However, this book is written under the belief that a quick review of mathematics as it was practiced for hundreds of years would be helpful for many students in understanding logarithms as they are still used today. The student quoted above was not instructed in a way that he internalized what logarithms are all about. It is a “readiness issue” which this book attempts to remedy.