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Re: combining Log[] terms
*To*: mathgroup at smc.vnet.net
*Subject*: [mg30506] Re: combining Log[] terms
*From*: "Souvik Banerjee" <s-banerjee at nwu.edu>
*Date*: Fri, 24 Aug 2001 04:06:07 -0400 (EDT)
*Organization*: Northwestern University, Evanston, IL, US
*References*: <9m281v$h28$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
The result is not true when one of a or b is negative. For example,
Log[-a], where a>0 can be written as Log[-1] + Log[a] = i Pi + Log[a] (using
DeMoivre's theorem). Hence, Log[-a] - Log[b] = i Pi + Log[a/b].
However, if both a and b are negative then the i Pi term cancels and you get
the same result.
Hence use either:
Simplify[Log[a] - Log[b], {b > 0, a > 0}] to get
Log[a/b].
or
Simplify[Log[a] - Log[b], {b < 0, a < 0}] to get
Log[a/b].
-Souvik
> Is there a function that combines terms like
>
> Log[a] - Log[b]
>
> to
>
> Log[a/b]?
>
> I couldn't find anything so far in the documentation regarding the
> Log[] function, only some references to Collect[], which does
> something similar to what I want for powers of a given expression.
>
> Thanks already for you help,
>
> nick
>
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