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MathGroup Archive 1999

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Re: Solving equations involving Ln function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19960] Re: Solving equations involving Ln function
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Wed, 22 Sep 1999 04:11:31 -0400
  • Organization: University of Western Australia
  • References: <7s1pb3$9n9@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Satyajit Bose wrote:

> I am trying to solve some equations involving the natural log function.
> Mathematica 3.0 will not let me solve them since the relations are
> non-algebraic. Is there any way to restrict the domain to positive reals
> or get Mathematica to use the exponential as an inverse, so that I can
> get a solution. I know that this can be done in another system, presumably
> because it is less careful about atypical domain restrictions.

Here is a Notebook snippet that solves this.

Notebook[{
Cell[BoxData[
    \(TraditionalForm\`\(\[ScriptCapitalE] = \[Delta]\ v + log(x) ==
          v\ \[Delta]\^2 + \(log(\(\((1 - \[Delta])\)\ \[Delta]\ x\)\/\(1 - \

\[Delta]\^2\))\)\ \[Delta] +
            log(\(\((1 - \[Delta])\)\ x\)\/\(1 - \[Delta]\^2\));\)\)], \
"Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(TraditionalForm\`Simplify[\[ScriptCapitalE], \[Delta] >
        0]\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`log(\[Delta] +
          1) == \[Delta]\ \((v\ \((\[Delta] - 1)\) +
            log(\(x\ \[Delta]\)\/\(\[Delta] + 1\)))\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(TraditionalForm\`Solve[%, x] // Simplify\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`{{x -> \(\[ExponentialE]\^\(v - v\ \[Delta]\)\ \((\
\[Delta] + 1)\)\^\(1 + 1\/\[Delta]\)\)\/\[Delta]}}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(TraditionalForm\`Simplify[\[ScriptCapitalE] /. First[%],
      v > 0 \[And] \[Delta] > 0]\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`True\)], "Output"]
}, Open  ]]
}
]

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia
Nedlands WA  6907                     mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________




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