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 ____________________________________________________________________