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000 + 00 = 00000

Logarithms **Explained**

**Logarithms - log tables - classic
oldfashioned conjuring trick for doing hard sums like magic. Take
two big numbers to be multiplied together, look up the magic code
numbers in the log-table, add the numbers, look up the magic
decode number from the anti-log table, and there's the answer!**

**(A quick note for those
born in the 21st Century and after: A long time ago, there were
no electronic calculators. To add up / multiply numbers manually
required a lot of work, but to multiply/divide was much more
difficult. Logs were a school technique where you could add up
some magic numbers looked up in a table of figures, and
mysteriously the decoded result would be the answer!)**

**Did you ever do logarithms? Did you
ever wonder how the "magic" worked? Did anyone ever
explain it? If you were born before a particular time ago,
chances are it's: YES,YES and NO.**

**Here's how it works:**

**Logarithms can multiply/divide any
numbers, usually things like 8472 x 6339, but suppose you were to
multiply as an example 1000 x 100. Obviously this is easy to do
in the head! But look at HOW you do it. You have THREE 0s and TWO
0s and you ADD them, get FIVE 0s, and so the answer is 100,000.**

**OK, so you add together how many 0s
there are. But the cunning trick of logarithms is that someone
found you could have HALF of a 0, or TWO AND A THIRD 0s, etc, and
add them up like that and get sensible answers! Half a 0 is the
SQUARE ROOT of 10 (because adding two of them makes ONE 0).**

**For any number you start with, there's
a "HOW MANY 0s" number, which is usually some funny
decimal. LOG(2) is 0.30103 (to five places). These are the
numbers you look up in the log-tables. What this means is that if
2 was a number with 1--- and so-many 0s it would have 0.30103 of
them. Sounds odd, but here's an example:**

**125 x 9972**

**125 . . . how many 0s has that got? If
it was 100 it would be 2.00000 precisely**

Log table reveals... LOG(125) = 2.09691

**9972 ... how many 0s? Nearly FOUR.**
(if it was 10,000 it would have exactly four zeros)

Log table reveals... LOG(9972) = 3.99878

**Add them together. 2.09691 + 3.99878 =
6.09569**

**The answer is going to be six-and-a-bit
0s. More than a million**

Looking it up in the anti-log table... Anti-log(6.09569) = 1246493

**So that's the answer to five decimal
places. So, 1246500 +- a bit.**

**(Logarithms are accurate to so-many
decimal places rather than absolutely precise. This is good for
engineering calculations where figures are within a working
tolerance)**

**Time taken to do the calculation: A lot
less than by long-multiplication. (but not as fast as using a
calculator!)**

**Was that explained well?
Or was it ****as
clear as mud****?
Do conjuring tricks of mathematics need explaining? It depends
whether you prefer to be mystified or to be a magician.**

**Logarithms have other
applications, for example ****deciBels**** are measured on a logarithmic
scale. The ****Richter Scale**** (for measuring earthquakes) is
also a logarithmic scale.**

**Yes, but what about ****Natural**** logarithms, log ****e**** ? And other log BASES? Can do!
See ****log
****e**

"Log Tables" were little books full of pages of tables of numbers. Typically a log-table book such as "Castle's Logs" would contain Sine tables as well, and all kinds of other data. It was hardly interesting bedtime-reading exactly, but then it was supposed to be reference rather than for reading through. I always thought the "physical constants" section was the most interesting, with such things as the mass of the earth, the electron charge, etc! Now a question often asked is: How did they first create these log tables of numbers, before computers? Well, shocking as it may seem, they did it by the very long-winded methods of manual calculation. There were a few clever shortcuts that made it easier, but it was still a vast amount of work. Historically, you can see it was done manually at first, as log tables can have a few small mistakes in them.

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Thanks and Well Done to Google for being sensible and starting to include this page again. Shame be upon Google for fowling up the page title! Note: Blekko gets this right! Even Bing gets this right! Yahoo lists the page but fowls up the title in a variant of the style Google does.