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 | | From: | Clive Ross | | Subject: | Logarithms...character and mantissa help | | Date: | Wed, 12 Jan 2005 19:56:41 -0500 |
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 | To those with knowledge:
Napier is credited for inventing logarithms. Immediately after, he and Biggs
began working on the development of log tables. At the same time, Galileo
was battling the Catholics on his/their theory of planet motion. He won and
the planets changed their course and began orbiting the Sun...coincidence of
course(s)...pun.
Back to Logs...
The of Log10 = 1, Log100 = 2, Log1000 = 3, etc... These we term as
"characters" of the exponent, but there are those numbers in-between these
integer values of base 10.
For these numbers the result is an exponent of two segments: the
"character" value" plus the "mantissa" (decimal segment).
An example...the Log25.119 = 1.400, the character is 1 and the mantissa is
0.400.
That part is easy...and my calculator tells me it's true.
Question...
What formula did Biggs and Napier use to determine/calculate the actual
value of the mantissa?
Thanks and await yours.
Clive
Life is not short...it is eternal.
It is we who have the short pleasure passing through it !
http://amitron2001.tripod.com/cgi-bin/all_topics.htm
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| | From: | Norbert Marrek | | Subject: | Re: Logarithms...character and mantissa help | | Date: | Thu, 13 Jan 2005 14:54:15 +0100 |
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"Clive Ross" wrote in message
news:byjFd.29486$b64.782211@news20.bellglobal.com...
> To those with knowledge:
>
> Napier is credited for inventing logarithms. Immediately after, he and
Biggs
> began working on the development of log tables. At the same time, Galileo
> was battling the Catholics on his/their theory of planet motion. He won
and
> the planets changed their course and began orbiting the Sun...coincidence
of
> course(s)...pun.
> Back to Logs...
>
> The of Log10 = 1, Log100 = 2, Log1000 = 3, etc... These we term as
> "characters" of the exponent, but there are those numbers in-between these
> integer values of base 10.
> For these numbers the result is an exponent of two segments: the
> "character" value" plus the "mantissa" (decimal segment).
> An example...the Log25.119 = 1.400, the character is 1 and the mantissa is
> 0.400.
> That part is easy...and my calculator tells me it's true.
>
> Question...
> What formula did Biggs and Napier use to determine/calculate the actual
> value of the mantissa?
>
> Thanks and await yours.
> Clive
> Life is not short...it is eternal.
> It is we who have the short pleasure passing through it !
> http://amitron2001.tripod.com/cgi-bin/all_topics.htm
>
>
They worked the other way: starting with 1.0001 = invlog(0.0001)
they multiplied 1.0001 with 1.0001 (rounding the result to 4 decimal places)
and added 0.0001 to 0.0001 over and over again.
This gives log(1.0001^10000) = 1 (natural logarithm basis e !)
They did not use the decimal logarithm.
Ciao,
Norbert
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| | From: | Clive Ross | | Subject: | Re: Logarithms...character and mantissa help | | Date: | Thu, 13 Jan 2005 11:41:25 -0500 |
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| Ciao:
I think I have a handle on your explanation. Your last statement "...This
gives log(1.0001^10000) = 1 (natural logarithm basis e !)..." took a
little time to work out.
But drifting away from Ln...how was the Log (base 10) system calculated?
Best.
Clive
Life is not short...it is eternal.
It is we who have the short pleasure passing through it !
http://amitron2001.tripod.com/cgi-bin/all_topics.htm
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| | From: | Clive Ross | | Subject: | Re: Logarithms...character and mantissa help | | Date: | Thu, 13 Jan 2005 22:49:03 -0500 |
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| Norbert:
Found the answer to the Log question.
Thanks for all and most appreciated.
Best.
Clive
Life is not short...it is eternal.
It is we who have the short pleasure passing through it !
http://amitron2001.tripod.com/cgi-bin/all_topics.htm
"Norbert Marrek" wrote in message
news:cs5ui8$k4n$1@news.mch.sbs.de...
>
> "Clive Ross" wrote in message
> news:byjFd.29486$b64.782211@news20.bellglobal.com...
> > To those with knowledge:
> >
> > Napier is credited for inventing logarithms. Immediately after, he and
> Biggs
> > began working on the development of log tables. At the same time,
Galileo
> > was battling the Catholics on his/their theory of planet motion. He won
> and
> > the planets changed their course and began orbiting the
Sun...coincidence
> of
> > course(s)...pun.
> > Back to Logs...
> >
> > The of Log10 = 1, Log100 = 2, Log1000 = 3, etc... These we term as
> > "characters" of the exponent, but there are those numbers in-between
these
> > integer values of base 10.
> > For these numbers the result is an exponent of two segments: the
> > "character" value" plus the "mantissa" (decimal segment).
> > An example...the Log25.119 = 1.400, the character is 1 and the mantissa
is
> > 0.400.
> > That part is easy...and my calculator tells me it's true.
> >
> > Question...
> > What formula did Biggs and Napier use to determine/calculate the actual
> > value of the mantissa?
> >
> > Thanks and await yours.
> > Clive
> > Life is not short...it is eternal.
> > It is we who have the short pleasure passing through it !
> > http://amitron2001.tripod.com/cgi-bin/all_topics.htm
> >
> >
>
> They worked the other way: starting with 1.0001 = invlog(0.0001)
> they multiplied 1.0001 with 1.0001 (rounding the result to 4 decimal
places)
> and added 0.0001 to 0.0001 over and over again.
>
> This gives log(1.0001^10000) = 1 (natural logarithm basis e !)
> They did not use the decimal logarithm.
>
>
> Ciao,
> Norbert
>
>
>
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