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Re: Are some equations unsolvable?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128072] Re: Are some equations unsolvable?
  • From: "Alexander Elkins" <alexander_elkins at hotmail.com>
  • Date: Thu, 13 Sep 2012 03:40:04 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • Delivered-to: l-mathgroup@wolfram.com
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  • References: <k2pc54$99t$1@smc.vnet.net>

One way to get a result is to rewrite f placing everything into Exp[] like
so:

In[1]:= FullSimplify[Log[(1/(sigma*Sqrt[2
Pi]))*Sqrt[(Pi/(-1/(2*sigma^2)))]]]
Out[1]= 1/2 (Log[-sigma] - Log[sigma])

In[2]:= Block[{f, m, sigma},
f = Exp[((m/sigma^2)^2)/4*(-1/2*sigma^2) + (m^2/(2*sigma^2)) +
1/2 (Log[-sigma] - Log[sigma])];
Solve[f == 216, sigma]]

(*Solve::ifun message*)

Out[2]= {{sigma -> -(((-1)^(1/4) m)/(
2 Sqrt[1/3 (\[Pi] + I Log[46656])]))}, {sigma -> ((-1)^(1/4) m)/(
2 Sqrt[1/3 (\[Pi] + I Log[46656])])}}

Note that Log[46656] == 2 Log[216].

Perhaps this helps...

"Sergio Sergio" <zerge69 at gmail.com> wrote in message
news:k2pc54$99t$1 at smc.vnet.net...
> Hi,
> This is what I have:
>
> f = (1/(sigma*Sqrt[2 Pi]))*Sqrt[(Pi/(-1/(2*sigma^2)))]*
>   Exp[((m/sigma^2)^2)/4*(-1/2*sigma^2) + (m^2/(2*sigma^2))]
>
> Solve[f == 216, sigma]
>
> And I get this message: "This system cannot be solved with the methods
available to Solve"
>
> Is it because there is no way to isolate sigma? Or am I doing something
wrong?
>
> Thanks
>





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