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Re: natural log of E

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg2017] Re: natural log of E
• From: wagner at bullwinkle.cs.Colorado.EDU (Dave Wagner)
• Date: Thu, 14 Sep 1995 23:29:11 -0400
• Organization: University of Colorado, Boulder

In article <DEKnts.Avv at wri.com>,
>
>I suspect that the reason that Mathematica is not able to
>interpret "Log[E^n]" as "n" might have to do with the fact that 
>"Log" is a multivalued function of its argument, and Mathematica 
>isn't able to decide on which Riemann sheet to put the answer.
>However, this isn't an entirely satisfactory answer, since when I  
>ask for "Log[E]", mm spits out "1" rather than "1 + 2 Pi I n_Integer"
>or somesuch.  /*shrug*/  Beats me.  I guess that's a question for 
>the experts.

ComplexExpand[Log[Exp[n]]] returns n.  The following command, which
tells ComplexExpand to treat n as a complex number, reflects the
multi-valued aspect of the Log function (albeit by expressing the
result in terms of another multi-valued function, ArcTan).

In[5]:=
ComplexExpand[Log[Exp[n]], n]
Out[5]=
I ArcTan[Cos[Im[n]], Sin[Im[n]]] + Re[n]

		Dave Wagner
		Principia Consulting
		(303) 786-8371
		dbwagner at princon.com
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