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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Question about logarithms
Replies: 29   Last Post: Sep 9, 2007 4:54 AM

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Oscar Lanzi III

Posts: 1,223
Registered: 12/12/04
Re: Question about logarithms
Posted: Sep 6, 2007 6:32 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

There is, actually, a number system in which the logarithm of -8 to the
base -2 comes out to be 3, and uniquely so.

That would be 3-adics. This is how it works: render the logarithm as
ln(-8)/ln(-2). Translate the arguments into 3-adics; each has the form
1+y where y ends with 0. Feed these into the Maclaurin series for
natural logarithms and observe that both series converge. Cancel out a
common terminal zero from the natural logarithms and do the division.
Voila, your quotient is ...000000010 which, in base ten, is 3.

In general, logarithms in p-adics may be defined for numbers ending with
1 in the p-adic representation (except p = 2 where you need ...01), and
they have all the properties of logarithms in more conventional systems.
I think it's pretty neat.

--OL
Date Subject Author
9/4/07
Read Question about logarithms
anja.ende@googlemail.com
9/4/07
Read Re: Question about logarithms
Jose Carlos Santos
9/4/07
Read Re: Question about logarithms
C6L1V@shaw.ca
9/4/07
Read Re: Question about logarithms
tommy1729
9/4/07
Read Re: Question about logarithms
David W. Cantrell
9/5/07
Read Re: Question about logarithms
tommy1729
9/5/07
Read Re: Question about logarithms
tommy1729
9/5/07
Read Re: Question about logarithms
David C. Ullrich
9/4/07
Read Re: Question about logarithms
Bart Goddard
9/4/07
Read Re: Question about logarithms
anja.ende@googlemail.com
9/4/07
Read Re: Question about logarithms
tommy1729
9/6/07
Read Re: Question about logarithms
b92057@yahoo.com
9/6/07
Read Re: Question about logarithms
C6L1V@shaw.ca
9/6/07
Read Re: Question about logarithms
b92057@yahoo.com
9/6/07
Read Re: Question about logarithms
tommy1729
9/6/07
Read Re: Question about logarithms
Oscar Lanzi III
9/7/07
Read Re: Question about logarithms
David W. Cantrell
9/7/07
Read Re: Question about logarithms
Oscar Lanzi III
9/4/07
Read Re: Question about logarithms
Stephen Montgomery-Smith
9/6/07
Read Re: Question about logarithms
b92057@yahoo.com
9/6/07
Read Re: Question about logarithms
Jose Carlos Santos
9/6/07
Read Re: Question about logarithms
b92057@yahoo.com
9/7/07
Read Re: Question about logarithms
Jose Carlos Santos
9/7/07
Read Re: Question about logarithms
b92057@yahoo.com
9/8/07
Read Re: Question about logarithms
Jose Carlos Santos
9/8/07
Read Re: Question about logarithms
b92057@yahoo.com
9/8/07
Read Re: Question about logarithms
Jose Carlos Santos
9/8/07
Read Re: Question about logarithms
b92057@yahoo.com
9/9/07
Read Re: Question about logarithms
Jose Carlos Santos
9/5/07
Read Re: Question about logarithms
b92057@yahoo.com

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