A Review Of Logarithms
Submitted by freefortermpapers on 06/24/2008 03:00 PM
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A Review Of Logarithms
A REVIEW OF LOGARITHMS
Many students in high school and in college have a difficult time with logarithms. In many cases, they memorize the rules without fully understanding them, and they sometimes even manage to squeak by a course. Why waste their time on these archaic entities; they are never going to see them again. Wrong! Just when the student breathes a sigh of relief to be done with logarithms, they encounter them again in another course. They are now in trouble because the second encounter with logarithms is at a more sophisticated level. Without an understanding of the basics, the student is doomed to blindly stumble through and fail the course. You have our sympathy and you have our solution. We at S.O.S. Math want you to succeed. We have prepared a review of logarithms for you with examples and problems. You can start at the beginning or jump in at any place.
Since logarithms are exponents, we will review exponential functions before we review logarithms and logarithmic functions. Before we review exponential functions, we will present a brief history of logarithms and a brief discussion of the functions.
History of Logarithms:
Logarithms were invented independently by John Napier, a Scotsman, and by Joost Burgi, a Swiss. The logarithms which they invented differed from each other and from the common and natural logarithms now in use. Napier's logarithms were published in 1614; Burgi's logarithms were published in 1620. The objective of both men was to simplify mathematical calculations. Napier's approach was algebraic and Burgi's approach was geometric. Neither men had a concept of a logarithmic base. Napier defined logarithms as a ratio of two distances in a geometric form, as opposed to the current definition of logarithms as exponents. The possibility of defining logarithms as exponents was recognized by John Wallis in 1685 and by Johann Bernoulli in 1694.
The invention of the common system of...
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