       Re: Help with Identities

• To: mathgroup at smc.vnet.net
• Subject: [mg65588] Re: Help with Identities
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Mon, 10 Apr 2006 02:31:08 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <e1ahdv\$2j1\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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)."

However,

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

returns the expression unevaluated

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

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

Out=
True

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

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

Out=
True

Best regards,
Jean-Marc

```

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