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MathGroup Archive 2003

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RE: This should evaluate to zero

  • To: mathgroup at
  • Subject: [mg39960] RE: [mg39926] This should evaluate to zero
  • From: "David Park" <djmp at>
  • Date: Thu, 13 Mar 2003 03:02:38 -0500 (EST)
  • Sender: owner-wri-mathgroup at


Mathematica doesn't simplify because there are multiple solutions.

You could do this..

ArcSinh[1] - Log[3363 + 2378*Sqrt[2]]/10 // N

But if you want to work with exact numbers do the following...

ArcSinh[1] - Log[3363 + 2378*Sqrt[2]]/10
% /. Log[a_] + b_*Log[c_] -> Log[a*c^b]


ArcSinh[1] - (1/10)*Log[3363 + 2378*Sqrt[2]]
Log[1 + Sqrt[2]] - (1/10)*Log[3363 + 2378*Sqrt[2]]
Log[(1 + Sqrt[2])/(3363 + 2378*Sqrt[2])^(1/10)]

Then it is clear that we have to find the 10th root of the denominator. It
turns out there are two real roots and only one positive real root. We can
select that and substitute with the following statement...

sols = First[Select[Solve[z^10 == 3363 + 2378*Sqrt[2]],
    With[{x = #1[[1,2]]}, Im[x] == 0 && Re[x] > 0] & ]]
Log[(1 + Sqrt[2])/z] /. sols

{z -> 1 + Sqrt[2]}

David Park
djmp at

From: jf alcover [mailto:jf.alcover at]
To: mathgroup at

Methinks that the following expression should evaluate to zero,
but it does not, even with FullSimplify :
Could anyone explain ?

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