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
>