Logarithms self-taught

133 Pages·1964·34.212 MB·English

by  Peter H Selby

Senior Research Engineer
General Dynamics/Astronautics
Formerly Flight Training Supervisor
Convair Division, San Diego
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McGraw-Hili Book Compony, New York· Toronto· London
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To
"Uncle Dudley"
who taught me to
enjoy mathematics
LOGARITHMS SELF-TAUGHT
Copyright © 1964 by McGraw-Hili, Inc.
All righh reserved, including the right to reproduce this book,
or any portion thereof, in any form, without permission by the
Publisher.
Printed in the United States of America
Library of Congress Catalog Card Number 64-16492
345678910 MUMU 7654321
ISBN 07-056068-4
PREFACE
You will find the material in this book presented in a different
way than you are accustomed to in an ordinary textbook. The
first thing you will notice is that you are given only a small
amount of information at a time, then immediately asked an
appropriate question to help you find out how much you have
understood, just as an individual tutor would do. The answer
you select in each case determines the item of information you
will be given next; hence your route through the course. This
is a special kind of self-teaching technique known as "pro
grammed instruction" or "auto-instruction."
Your rate of progress-the time you spend and the amount of
material you read-is, therefore, up to you. You can go as rapidly
or as slowly as your aptitude and inclination permit.
If this is the first time you have studied a subject presented
in this new way, you should find it an interesting way to learn.
Whom This Course Is For
This book is intended primarily for the following two groups:
1. Those individuals who want or need to know something about
the practical techniques of solving mathematical problems
which require, or can be simplified by the use of, logarithms
(either numerical or trigonometric) and who are approaching
this subject for the first time.
2. Those who may have learned something about logarithms in
high school or college (perhaps a long while ago), but who
have had little occasion to use their knowledge since and now
need a brief review of the subject in order to apply it in their
work or to further study.
CONTENTS
Preface
Whom This Course Is For
What You Can Expect to Learn from This Course
What the Reader Needs to Know about This Book
Part I. Logarithms of Numbe"
Exponents 5
What Logarithms Are 8
Use of the Numerical Log Tables 14
Determining the Characteristic of a Number 18
The Two Parts of a Log 19
Practice in Finding Logarithms 26
Rule for Determining the Characteristic 29
Rules Governing Exponents (Logs) 30
Practice Problems 41
Review of Numerical Logs 42
Part II. Trigonometry and Logarithms Combined 44
Use of the Log-Trig Tables 49
A Sample Problem 50
Some Practice Problems 54
Final Review 55
Self-quiz 57
Numerical Logs 57
Log Trigonometry 61
Answers to Self-quiz 63
Glossary of Terms 66
Supplementary Problems 68
Appendix A. Logarithms of Selected Numbe" 73
Appendix B. Logarithms of the Trigonometric Functions 76
What You Can Expect to Learn from This Course
This specialized course of instruction is by no means all
inclusive. It is intended to familiarize you with the basic con
,-'epts underlying the use of logarithms, both numerical and
trigonometric, and to assist you in learning how to apply these
concepts in solving problems.
Specifically, at the conclusion of this course, you should be
generally familiar with the theory and use of common logarithms
and the practical techniques of solving plane right triangles with
the aid of a table of logarithms of the trigonometric functions.
You should also be able to demonstrate your knowledge by scor
ing at least 40 on the self-administered quiz found at the back of
this book.
It is assumed that the reader has had a first course in algebra
and a course in trigonometry at some time in his educational
career. However, the author has endeavored to explain all
needed terms and concepts herein. (Be sure to look in the
Glossary, page 66, for an explanation of any words or expressions
that are not familiar to you. )
You will not need to have studied trigonometry in order to
understand the explanation concerning the theory and use of
common logarithms. However, if you wish to gain a working
knowledge of how logarithms of the trigonometric functions are
used to aid in the solution of problems in trigonometry, then you
may wish to procure a copy of "Trigonometry Self-Taught," a
companion volume which will supply the necessary background
for this course, or to take one of the courses in trigonometry
available through schools.
If a general familiarity with the theory and use of logarithms
is as much as you want (or need), practicing what this program
will teach you should in time make you skillful in using logarithms
to solve practical problems in multiplication, division, raising
numbers to higher powers, or extracting roots. You also will
develop a practical skill in solving plane right triangles through
the use of logarithms.
On the other hand, if finishing this program merely whets
your appetite-so that you want to learn more about logarithms,
other applications and other kinds of logarithms-then by all
means seek out a good teacher and a good standard textbook.
This program will at least have served to start you on a fascinating
highway that you can follow as far as you care to travel.
What the Reader Needs to Know about This Book
This is no ordinary book. Although the pages are num
bered consecutively, they are not intended to be read consecu
tively.
At the bottom of each page, you will be told which page to
turn to next. Follow these instructions and you will have no
trouble staying on the intended path. This will aid us in present
ing just the information you need to help you understand the
subject matter.
To begin, proceed to page 1.
Part I
Logarithms of Numbers
Anyone who has ever had occasion to multiply 6.41 X 0.00127
X 6984.3 X 1.002, and then possibly divide the product by 974.2 X
0.0394, is in the market for logarithms (or "logs" as the name
usually is abbreviated) whether he knows it or not. They are of
considerable aid in multiplying, dividing, and raising numbers to
higher powers.
As a word of encouragement, if you have not hitherto been
exposed to the subject, or if you have been dazzled by its
imagined difficulties, do not be afraid! There is nothing very
mysterious about logs. They are not a disease (not in the ordi
nary sense at least) and, in any case, not a contagious one.
Perhaps you have learned something about them already.
Let's see if you can pick the best answer to this question: Of
what use are logarithms?
Logarithms aid in the multiplication and division
of numbers. PAGE 5
Logarithms can be used to add long sums of
numbers quickly. PAGE 3
I can't answer because I don't know what a log-
arithm is. PAGE 7