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 ?