       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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