Do this (without a calculator!)

42.5 x 37.6

A blast from the past

Slide Rules

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.

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.

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 =

Source: http://www.sliderule.ca/intro.htm

How do logs help in multiplication?

2 x 3 = yLog (2 x 3) = log y

Log 2 + log 3 = log y.301 + .477 = log y

.778 = log y10.778 = y

y = 6

To find log x:1. Line up cursor with x on D scale2. Read number on L scale3. Add “1” to your answer for each

number past the ones place

Ex. Find log 25Line up cursor with 2.5 on D scaleRead number on L scaleBecause there’s a number in the 10’s spot,

add 1.

Use the slide rule to find the following logs.

1. Log 32. Log 83. Log 1.24. Log 385. Log 526. Log 135

What number has a log of. . .

1. 0.62. 1.373. 2.2

To multiply (xy):1. Line up "1" of C scale with x

on D scale2. Set hairline of cursor over y on

C scale.3. Answer is number on D scaleEx. Multiply 2x3:Line up "1" on C scale with 2 on D-scaleMove cursor to 3 on C scaleRead # on D scale

Do these:1. 15 x 42. 18 x 3.73. 1.5 x 2.34. 280 x 0.345. .0215 x 3.54

To divide ( x ÷ y ):1. Line up x on D scale with y on

C scale.2. Answer lines up with “1” on D

scale.Ex. Divide 8 ÷ 43. Line up 8 on D scale with 4 on C scale4. Move cursor to 1 on C scale5. Read # on D scale

Do these:1.15 ÷ 32.62.4 ÷ .7073.23 ÷ 1.64.0.53 ÷ 7

Combining Operations 1. Think of problem as 2. Line up x on D scale with z on

C scale3. Move cursor to y on C scale4. Read answer on D scale

Do these: 1.

2.

3.

4.