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Unlock the Power of Slide Rules: A Dive Into Logarithms

Discover the history and practical use of slide rules and logarithms. Learn how to multiply, divide, and combine operations using this fascinating tool. No calculator needed! Dive into the world of numbers with this insightful guide.

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Unlock the Power of Slide Rules: A Dive Into Logarithms

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  1. Do this (without a calculator!) 42.5 x 37.6

  2. Slide Rules A blast from the past

  3. Logarithms were invented by the Scottish mathematician and theologian John Napier and first published in 1614. He was looking for a way of quickly solving multiplication and division problems using the much faster methods of addition and subtraction. Napier's way of doing this was to invent a group of "artificial" numbers as a direct substitute for real ones.

  4. He called this numbering system logarithms (which is Greek for "ratio-number", apparently). Logarithms are consistent, related values which substitute for real numbers. Incidentally, it wasn't until a few years later, in 1617, that a fellow mathematician named Henry Briggs adapted Napier's original "natural" logs to the more commonly used and convenient base 10 format.

  5. Source: http://www.sliderule.ca/intro.htm • To see how these are useful for multiplication, consider what happens if you want to multiply 10 x 1,000, as a simple example. The secret here is that you could just add their logs together and then take the anti-log of the result. • Why? Because log xy =

  6. How do logs help in multiplication? 2 x 3 = y Log (2 x 3) = log y Log 2 + log 3 = log y .301 + .477 = log y .778 = log y 10.778= y y = 6

  7. To find log x: 1. Line up cursor with x on D scale 2. Read number on L scale 3. Add “1” to your answer for each number past the ones place Ex. Find log 25 Line up cursor with 2.5 on D scale Read number on L scale Because there’s a number in the 10’s spot, add 1.

  8. Use the slide rule to find the following logs. 1. Log 3 2. Log 8 3. Log 1.2 4. Log 38 5. Log 52 6. Log 135

  9. What number has a log of. . . 1. 0.6 2. 1.37 3. 2.2

  10. To multiply (xy): • Line up "1" of C scale with x on D scale • Set hairline of cursor over y on C scale. • Answer is number on D scale Ex. Multiply 2x3: Line up "1" on C scale with 2 on D-scale Move cursor to 3 on C scale Read # on D scale

  11. Do these: • 15 x 4 • 18 x 3.7 • 1.5 x 2.3 • 280 x 0.34 • .0215 x 3.54

  12. To divide ( x ÷ y ): • Line up x on D scale with y on C scale. • Answer lines up with “1” on D scale. Ex. Divide 8 ÷ 4 • Line up 8 on D scale with 4 on C scale • Move cursor to 1 on C scale • Read # on D scale

  13. Do these: • 15 ÷3 • 62.4 ÷ .707 • 23 ÷ 1.6 • 0.53 ÷ 7

  14. Combining Operations • Think of problem as • Line up x on D scale with z on C scale 3. Move cursor to y on C scale 4. Read answer on D scale

  15. Do these: 1. 2. 3. 4.

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