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RE: This should evaluate to zero
*To*: mathgroup at smc.vnet.net
*Subject*: [mg39960] RE: [mg39926] This should evaluate to zero
*From*: "David Park" <djmp at earthlink.net>
*Date*: Thu, 13 Mar 2003 03:02:38 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
jf,
Mathematica doesn't simplify because there are multiple solutions.
You could do this..
ArcSinh[1] - Log[3363 + 2378*Sqrt[2]]/10 // N
0.
But if you want to work with exact numbers do the following...
ArcSinh[1] - Log[3363 + 2378*Sqrt[2]]/10
TrigToExp[%]
% /. Log[a_] + b_*Log[c_] -> Log[a*c^b]
giving
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]}
0
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: jf alcover [mailto:jf.alcover at bdpme.fr]
To: mathgroup at smc.vnet.net
Bonjour,
Methinks that the following expression should evaluate to zero,
but it does not, even with FullSimplify :
ArcSinh[1]-Log[3363+2378*Sqrt[2]]/10
Could anyone explain ?
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