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[1]:=
Log[x/y] == Log[x] - Log[y]
returns the expression unevaluated
Out[1]=
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[2]:=
Simplify[Log[x/y] == Log[x] - Log[y],
Assumptions -> x > 0 && y > 0]
Out[2]=
True
or we can use *PowerExpand* that makes this kind of assumptions for us
In[3]:=
PowerExpand[Log[x/y] == Log[x] - Log[y]]
Out[3]=
True
Best regards,
Jean-Marc