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

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

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Jonathan Hoyle

Posts: 398
Registered: 12/10/04
Re: ln(x^x)
Posted: May 9, 2000 4:31 PM
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>> 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

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