Re: Simplifying Log[a] + Log[expr_] - Log[2 expr_]: Brute force necessary?
- To: mathgroup at smc.vnet.net
- Subject: [mg81693] Re: Simplifying Log[a] + Log[expr_] - Log[2 expr_]: Brute force necessary?
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Tue, 2 Oct 2007 05:23:11 -0400 (EDT)
- Organization: The Open University, Milton Keynes, UK
- References: <fdqclq$mmg$1@smc.vnet.net>
W. Craig Carter wrote:
> This works as I would hope it would:
>
> Simplify[Log[a^2] + Log[b^2] - Log[-2 b^2],
> Assumptions -> Element[a, Reals] && Element[b, Reals]]
>
> It returns -Log[-2/a^2]
>
> However, something a little more complicated:
>
> Simplify[
> Log[4] -
---------^
Too many minus signs.
> - 2 Log[-2 ((R + x)^2 + y^2 + (z - zvar)^2)]
> + 2 Log[(R + x)^2 + y^2 + (z - zvar)^2]),
------------------------------------------------^
Extraneous parenthesis.
> Assumptions ->
> {Element[zvar,Reals], Element[x,Reals],Element[y, Reals], Element[z, Reals}]
----------------------------------------------------------------------------^
Missing square bracket.
>
> doesn't simplify. I can't see a way to do this, but brute force.
>
> Any ideas?
Fixing the syntax errors and adding the parameter R in the list of real
argument does not help. You could use *ComplexExpand*.
In[1]:= Simplify[
Log[4] - 2 Log[-2 ((R + x)^2 + y^2 + (z - zvar)^2)] +
2 Log[(R + x)^2 + y^2 + (z - zvar)^2],
Assumptions -> Element[{R, zvar, x, y, z}, Reals]]
Out[1]= Log[4] - 2 Log[-2 ((R + x)^2 + y^2 + (z - zvar)^2)] +
2 Log[(R + x)^2 + y^2 + (z - zvar)^2]
In[2]:= ComplexExpand[
Log[4] - 2 Log[-2 ((R + x)^2 + y^2 + (z - zvar)^2)] +
2 Log[(R + x)^2 + y^2 + (z - zvar)^2]]
Out[2]= -2 \[ImaginaryI] \[Pi] - 2 Log[2] + Log[4]
HTH,
--
Jean-Marc