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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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