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Re: Why doesn't Log[ E^x ] = x ?

• To: mathgroup at smc.vnet.net
• Subject: [mg24241] Re: Why doesn't Log[ E^x ] = x ?
• From: "Kevin J. McCann" <kevinmccann at home.com>
• Date: Tue, 4 Jul 2000 15:22:05 -0400 (EDT)
• References: <8jrdc2$e2t@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Because the Log, considered as a complex function, is multivalued. E.g.

Log[E^2]=2
but
Log[E^(2+2Pi I)]=2
that is Mathematica's answer, rather than (2+2Pi I) which is not on the principle
branch. And
Log[E^(I 2Pi)]=0
not I 2Pi

When you try

Log[E^x]

Mathematica doesn't know enough about x to answer; so it doesn't.

Kevin

"Christopher R. Carlen" <crcarle at sandia.gov> wrote in message
news:8jrdc2$e2t at smc.vnet.net...
> Hi:
>
> E^Log[x] evaluates to x
>
> but
>
> Log[ E^x ] evaluates to Log[ E^x ]
>
> Why?
>
> Thanks.
>
> P.S.  Mathematica 3.0
>
> _______________________
> Christopher R. Carlen
> Sr. Laser/Optical Tech.
> Sandia National Labs
>