Napier’s Bones and the Amazing Logarithmic Function - PowerPoint PPT Presentation

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Napier’s Bones and the Amazing Logarithmic Function

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  1. Napier’s Bones and the Amazing Logarithmic Function Chapter 6.7…

  2. The first European “calculator”? • The Logarithm was introduced by John Napier in 1614. It was intended to make complex arithmetic calculations “easier”. • In Napier’s words…

  3. Seeing there is nothing (right well-beloved Students of the Mathematics) that is so troublesome to mathematical practice, nor that doth more molest and hinder calculators, than the multiplications, divisions, square and cubical extractions of great numbers, which besides the tedious expense of time are for the most part subject to many slippery errors, I began therefore to consider in my mind by what certain and ready art I might remove those hindrances. And having thought upon many things to this purpose, I found at length some excellent brief rules to be treated of (perhaps) hereafter. But amongst all, none more profitable than this which together with the hard and tedious multiplications, divisions, and extractions of roots, doth also cast away from the work itself even the very numbers themselves that are to be multiplied, divided and resolved into roots, and putteth other numbers in their place which perform as much as they can do, only by addition and subtraction, division by two or division by three.

  4. Review of the “Log” function and its rules • Logs and bases • Multiplying/Dividing • Powers • Logs and Inverses Maple tip: use log[b](x) to find the log of x in base ‘b’

  5. The derivative of “Log” and proof that God does NOT have 10 fingers! • Finding the slope via the Newton Quotient • A famous limit • Why the Natural log (ln) is natural and Log10 is Not! • Integral definition of ln(x) Pg 465-466: 12, 23, 31,36,37