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Re: Log[Exp[r]] <> r?

• To: mathgroup at smc.vnet.net
• Subject: [mg39279] Re: Log[Exp[r]] <> r?
• From: "Kevin J. McCann" <KevinMcCann!kjm at uunet.uu.net>
• Date: Sun, 9 Feb 2003 04:50:17 -0500 (EST)
• References: <b22jou$6bh$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

It is because the log is a multivalued function. I believe that Log gives
the principle branch, i.e. -Pi < Arg[Log[z]] < Pi; equivalently, the branch
cut is chosen to go from 0 to -Infinity (real). This may be illustrated by

Log[Exp[2+4.5*Pi*I]]

which returns 2.0+1.5708I. it does not return 2+4.5*Pi*I, rather 2+0.5*Pi*I
which is in the principle branch.

Kevin

"Jonathan Greenberg" <greenberg at ucdavis.edu> wrote in message
news:b22jou$6bh$1 at smc.vnet.net...
> Hi there, why is it when I enter Log[Exp[r]] (or use Simplify or
> FullSimplify) I don't get r?  If I do Log[Exp[2]] I get 2!
>
> --j
>
> --
> Jonathan Greenberg
> Graduate Group in Ecology, U.C. Davis
> http://www.cstars.ucdavis.edu/~jongreen
> http://www.cstars.ucdavis.edu
> AIM: jgrn307 or jgrn3007
> MSN: jgrn307 at msn.com or jgrn3007 at msn.com
>
>