From: nma@12000.org   
      
   On 4/17/2017 11:22 AM, clicliclic@freenet.de wrote:   
      
   >>   
   >> btw, on the ln(x^2)=2*ln(x) issue. Could this be resolved by   
   >> changing it to   
   >>   
   >>           ln(x^2) = 2*ln(|x|)   
   >>   
   >> Mathematica seems to agree   
   >>   
   >> Simplify[Log[x^2]-2 Log[Abs[x]]]   
   >>     0   
   >>   
      
   >   
   > Zero also results on Derive 6.10 for the default assumption of real x,   
   > but not for complex x, where the two logarithmic terms surely differ;   
   > at x = #i one finds:   
   >   
   >   LN(#i^2) - 2*LN(ABS(#i)) = LN(-1) - 2*LN(1) = pi*#i - 0   
   >   
      
   Opps, good point. I did not think that x can be complex :)   
   So I assume this is why Maple did not simplify   
      
   simplify(ln(x^2)-2*ln(abs(x)),ln);   
      
   to zero like Mathematica did.   
      
   But then why when I now tell Maple that x is real, it still does   
   not simplify the above to zero?   
      
   assume(x::real);   
   simplify(ln(x^2)-2*ln(abs(x)),ln);   
      
                          ln(x~^2)-2*ln(abs(x~)) # why not zero now?   
      
   about(x);   
   Originally x, renamed x~:   
      is assumed to be: real   
      
   Should then Maple have simplified it to zero now that it was   
   told x is real?   
      
   > for example. Since bugs as basic as yours should be rare in a mature   
   > system like Mathematica, I prefer to assume that your x was somehow   
   > implied to be real, perhaps because you defined it that way and forgot.   
   >   
   > Martin.   
   >   
      
   Yes, I must have done something silly, as I can't reproduce it   
   on fresh kernel. I must have assumed x is real as you said   
   and did not notice.   
      
   On fresh kernel, Mathematica does indeed simplify it to zero,   
   only with the assumption that x is real (unlike Maple)   
      
   Clear[x]   
   Assuming[Element[x,Reals],FullSimplify[Log[x^2]-2*Log[Abs[x]]]]   
   Out[14]= 0   
      
   The question then   
   =================   
      
   Why Maple does not simplify it to zero   
   now that it is told x is real? Is there any other more advanced   
   subtle math involved that Maple knows about?   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)