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MathGroup Archive 2006

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Re: Help with Identities

  • To: mathgroup at
  • Subject: [mg65588] Re: Help with Identities
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at>
  • Date: Mon, 10 Apr 2006 02:31:08 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <e1ahdv$2j1$>
  • Sender: owner-wri-mathgroup at

Sven C. Koehler wrote:
> Hello!
> As an occasional mathematican, I sometimes forget that i.e.
> Log[x/y] is very similar to Log[x] / Log[y]
> Is there some way in Mathematica to see how an mathematical
> expression could look like alternatively?  (Something like the  opposite
> of Simplify.)
> And then I wonder why 
> Log[x/y] === Log[x] - Log[y]
> is False.  Can I instruct Mathematica to explain why this is False?
> Best wishes,
> Sven
Hi Sven,

According to _The Mathematica Book_, 5th Ed., "You should typically use 
=== when you want to test the structure of an expression, and == if you 
want to test mathematical equality (Section 2.6.8)."


Log[x/y] == Log[x] - Log[y]

returns the expression unevaluated

Log[-] == Log[x] - Log[y]

Mathematica works by default with complex numbers; therefore we must use 
some assumptions that indicates that x and y are positive real variables 
as in

Simplify[Log[x/y] == Log[x] - Log[y],
   Assumptions -> x > 0 && y > 0]


or we can use *PowerExpand* that makes this kind of assumptions for us

PowerExpand[Log[x/y] == Log[x] - Log[y]]


Best regards,

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