Logarithm

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Contents
Introduction 1
Evolution of Logarithmic Concepts 2
John Napier of Merchiston 3
Early Life 3
Advances in Mathematics 3
Napier’s Logarithm Table 4
Initial ideas 4
Progression of Arithmetic and Geometric concepts 4
Definition of the Logarithm 4
Approximation of the Logarithm 4
Construction of the table 4
Base of Logarithms 4
Logarithms of Negative Numbers 5
Methodology 5
Controversy 5
Euler’s Take 5
Conclusion 6
References 6

Introduction
The contemporary world is full of marvels. Technological advances have enabled mankind to fly in the heavens, instantaneously communicate with distant relatives thousands of miles away, construct buildings that are able to withstand many natural disasters, cure deadly diseases, and even travel to and study areas beyond the confines of planet Earth. While there are many factors that contributed to man’s ability to overcome what many once thought were impossible feats, it is the study of engineering that has enabled one to study the elements and leverage all that they have to offer. Mathematics lies at the heart of all science, including engineering. Without progressions in mathematical concepts, engineering principles and applications would not have advanced as quickly as they have throughout history.
No concept has had such a profound impact on mathematics (and in turn, engineering) than Logarithms. Logarithms are an essential part of numerous facets of modern technology. While logarithms have been embedded in the world of mathematics for numerous centuries, the concept has notoriously changed and evolved rather quickly as well. As one learns about the developmental history behind logarithms, its effect, importance, and relevance on contemporary engineering will become clearer. The...

... middle of paper ...

...logarithm. Napier actually calculated these entries in the opposite manner, however. He generated a list of logarithms first and then selected those values that corresponded to a sine of an arcminute. Figure 4 demonstrates how Napier may have computed values for his table and Figure 5 shows the first page of Napier’s table of logarithms (Clark, 2001).

Figure 4. Napier’s Logarithm Calculations (Clark, 2001)

Figure 5. Napier’s Logarithm Table – Page 1 (Clark, 2001)
A completed table of logarithms

BASE OF LOGARITHMS
Logarithms of Negative Numbers
1.1 Unqualified Opinion
1.2 Qualified Opinion Report
1.3 Adverse Opinion Report
1.4 Disclaimer of Opinion Report
1.5 Auditor’s Report on Internal Controls of Public Companies
1.6 Going Concern
METHODOLOGY
CONTROVERSY
EULER’S TAKE
Conclusion
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