Re: solving non-algebraic exponential equations
- To: mathgroup at smc.vnet.net
- Subject: [mg38131] Re: [mg38059] solving non-algebraic exponential equations
- From: Vladimir Bondarenko <vvb at mail.strace.net>
- Date: Tue, 3 Dec 2002 04:34:12 -0500 (EST)
- In-reply-to: <200211281908.OAA23991@smc.vnet.net>
- References: <200211281908.OAA23991@smc.vnet.net>
- Reply-to: Vladimir Bondarenko <vvb at mail.strace.net>
- Sender: owner-wri-mathgroup at wolfram.com
eva.hoehberger at gmx.net (Eva Hohberger) wrote on Thursday, November 28, 2002, 3:08:00 PM :
EH> I am trying to solve the following equation for given values of two
EH> parameters a and b:
EH> NSolve[Exp[-Pi*a/x] + Exp[-Pi*b/x] == 1, x]
EH> This is straightforward for integer values of the parameters a and b
EH> (e.g. a=1, b=1). However, Mathematica is unable to compute the
EH> solution for non-integer values of a and b (e.g. a=1.1, b=1.1; even
EH> a=1.0, b=1.0 doesn't work). Instead, the error message "Solve::"tdep":
EH> "The equations appear to involve the variables to be solved for in an
EH> essentially non-algebraic way." is produced.
EH> Can anybody point out a way to overcome this problem and to obtain a
EH> solution?
Your may wish to use FindRoot.
a = 1.1; b = 1.1;
FindRoot[Exp[-Pi*a] + Exp[-Pi*b/x] == 1, {x, 1/10^100, 10}]
{x -> 107.748}
a = Random[Real, 1, 1000];
b = Random[Real, 1, 1000];
FindRoot[Exp[-Pi*a] + Exp[-Pi*b/x] == 1, {x, 1/10^100, 10}]
{x -> 0.741772}
Best wishes,
Vladimir Bondarenko
Mathematical and Production Director
Symbolic Testing Group
http://www.CAS-testing.org/ GEMM Project (95% ready)
Email: vvb at mail.strace.net
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