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Re: Re: Re: Simplifying Log[a] + Log[expr_] -

• To: mathgroup at smc.vnet.net
• Subject: [mg81878] Re: [mg81843] Re: [mg81803] Re: Simplifying Log[a] + Log[expr_] -
• From: "W. Craig Carter" <ccarter at mit.edu>
• Date: Fri, 5 Oct 2007 04:58:29 -0400 (EDT)
• References: <fdqclq$mmg$1@smc.vnet.net> <200710031033.GAA26771@smc.vnet.net>

>>
>> You can use a rule to bring everything under one Log:
>>
>> LogZusammenRule={
>>   n_. Log[a_]+m_. Log[b_]:>Log[a^n b^m],
>>   n_. Log[a_]-m_. Log[b_]:>Log[a^n/b^m],
>>   a_ Log[b_]:>Log[b^a] };
>
>  ComplexExpand[-2*Log[-2*((R + x)^2 + y^2 + (z - zvar)^2)] +
>   2*Log[(R + x)^2 + y^2 + (z - zvar)^2]]
>  -2*I*Pi - 2*Log[2]


Thanks everyone. I view the rules as brute force (but that 
is a matter of taste, not a disparaging comment on the 
useful help). In the complexexpand example, I had to do this:
ComplexExpand[FullSimplify[logexpression,Assumptions->assumptions]]
to get the result that I wanted (which was Sqrt[-1] Pi)

• References:
  • Re: Simplifying Log[a] + Log[expr_] - Log[2 expr_]: Brute force necessary?
    • From: Peter Breitfeld <phbrf@t-online.de>