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Topic: Are some equations unsolvable?
Replies: 3   Last Post: Sep 13, 2012 3:43 AM

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Alexander Elkins

Posts: 32
Registered: 4/13/09
Re: Are some equations unsolvable?
Posted: Sep 13, 2012 3:43 AM
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One way to get a result is to rewrite f placing everything into Exp[] like

In[1]:= FullSimplify[Log[(1/(sigma*Sqrt[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" <> wrote in message
> 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

> Thanks

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