|
|
![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Message
|
|
|
| ``Re: Logarithms: Something more is needed''
by rspuzio on 2008-06-13 12:17:28 |
|
| > But what I don't understand is: how did they step the result back up?
They did that by looking a the logarithm table backwards or, if they had
an antilogarithm table, by looking at that. Let me illustrate with an
example. Suppose we want to multiply 17.81 by 6.520. Whipping out
the old log table (and blowing the dust off it nowadays), I find that
the base 10 logarithms of these numbers are 1.25066 and 0.81425.
Adding them produces 2.06491. To step the result back up, I look in
the table for the logarithm closest to 0.06491 and find that
log 1.161 = 0.06521 so the answer is 116.1 to four digits.
> Even with base 10 logarithms, the result would often be a number with
> a fractional part, so getting the result wouldn't be as easy as
> writing a bunch of zeroes after a one.
As shown in the example above, the fractional part would be dealt with
by looking in the table backwards to find a number between 1 and
10 whose logarithm is closest to the fractional part of the result.
Then obtaining the result is a matter of taking into account the
integer part by adding zeros and shifting the decimal point
appropriately.
> So something is missing in this picture.
It would be good if that something were explained in the entry on
logarithm tables. Along those lines, I would suggest the following
improvements. Change the title to "logarithm tables", then add
a short table of base 10 logarithms and add some text explaining
how log tables were used to multiply and divide numbers in the
old days. While this may not be of much contemporary relevance, it
is a part of the recent history of mathematics, so it definitely
is worth describing in order to round out our account of math. |
| | [ reply | up | top ] | |
|
|
|
|
|
|
|
