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Re: Working with Log

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112113] Re: Working with Log
  • From: Patrick Scheibe <pscheibe at trm.uni-leipzig.de>
  • Date: Tue, 31 Aug 2010 04:16:17 -0400 (EDT)

Hi,

there's no unexpand but to know that PowerExpand uses heavy assumptions
per default is useful. This should be a warning too that the results of
PowerExpand not in general true. See for instance what

PowerExpand[Log[a b], Assumptions -> Element[{a, b}, Complexes]]

gives:

2*I*Pi*Floor[1/2 - Arg[a]/(2*Pi) - Arg[b]/(2*Pi)] + Log[a] + 
   Log[b]

Your expansion is valid for instance for 

PowerExpand[Log[a b], Assumptions -> a > 0 && b > 0]

and therefore

FullSimplify[%, Assumptions -> a > 0 && b > 0]

gives again

Log[a b]

To see where exactly the log rule works you could do maybe

Reduce[2*I*Pi*Floor[1/2 - Arg[a]/(2*Pi) - Arg[b]/(2*Pi)] == 0, {a, b}]

Cheers
Patrick



On Mon, 2010-08-30 at 06:20 -0400, Themis Matsoukas wrote:
> I can use PowerExapnd to expand a Log:
> 
> PowerExpand[Log[a b]]
> 
> Log[a] + Log[b]
> 
> How can I do the opposite, i.e. combine Log[a] + Log[b] into Log[a b]?
> 
> Thanks
> 
> Themis
> 



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