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Topic: ln(x^x)
Replies: 22   Last Post: May 10, 2000 5:27 PM

 Messages: [ Previous | Next ]
 Jonathan Hoyle Posts: 398 Registered: 12/10/04
Re: ln(x^x)
Posted: May 9, 2000 4:31 PM

>> Alright. For the purposes of Calc I, they're the same.

Moving into the complex plane, the better question is to ask when does
ln(z^z) = zln(z)? Obviously it holds for all positive reals, and it's
easy enough to find a counterexample: z = -2:

ln(z^z)
= ln((-2)^(-2))
= ln(1/((-2)^2))
= ln(1/4)
= -ln(4)

zln(z)
= -2*ln(-2)
= -2*(ln(2) + ipi)
= -2*ln(2) - 2ipi
= -ln(4) - 2ipi

Date Subject Author
5/6/00 \
5/6/00 Doug Norris
5/6/00 SirWobbly
5/8/00 anonymous
5/9/00 Didier Bizzarri
5/9/00 G. A. Edgar
5/9/00 anonymous
5/9/00 Jonathan Hoyle
5/9/00 Jonathan Hoyle
5/10/00 Robert Israel
5/6/00 Clive Tooth
5/6/00 J. Mayer
5/6/00 Fred W. Helenius
5/6/00 Doug Norris
5/6/00 Richard Carr
5/6/00 Doug Norris
5/9/00 Jonathan Hoyle
5/6/00 David Swanson
5/7/00 Herman Rubin
5/6/00 Stephen Norris
5/6/00 Zdislav V. Kovarik
5/7/00 Oscar Lanzi III
5/8/00 Bob Silverman