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Re: Problem solving equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg40745] Re: Problem solving equation
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 16 Apr 2003 01:34:47 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <b7gfe0$eba$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

since when is

Log[a+b] == Log[a]+Log[b]

?
The correct form of

> Log[1.046*Exp[.0151*t]] + Log[1.284*Exp[.0087*t]] == Log[6.3]

Log[1.046*Exp[.0151*t] + 1.284*Exp[.0087*t]] == Log[6.3]

an that's all. You can factor one exponential term but
it still remain that you have to solve a equation like

d*t +Log[b+a Exp[q *t]]== c

and this can't be done by hand/analytical.

Regards
  Jens

Heath wrote:
> 
> Hi,
> I'm trying to solve the following equation:
> 
> Solve[1.046*Exp[.0151*t] + 1.284*Exp[.0087*t] == 6.3, t]
> 
> and am getting this error message:
> 
> Solve::"tdep": "The equations appear to involve the variables to be
> solved \
> for in an essentially non-algebraic way."
> 
> I cannot solve it with Solve[] or NSolve[].
> I was able to find the solution by using Plot[] to get an idea where
> the solution is, followed by FindRoot[].
> 
> Why doesn't the expression simplify to, as I believe it does on paper,
> to:
> Log[1.046*Exp[.0151*t]] + Log[1.284*Exp[.0087*t]] == Log[6.3]
> Log[1.046]+Log[Exp[.0151*t]]+Log[1.284]+Log[Exp[.0087*t]]==Log[6.3]
> Log[1.046*1.284]+.0151*t+.0087*t==Log[6.3]
> .0238*t==Log[6.3]-Log[1.046*1.284]
> .0238*t==Log[6.3/(1.046*1.284)]
> .0238*t==1.545596
> t==64.94
> 
> This "hand" solution is not the same as the solution I get using
> FindRoot[] in Mathematica. Mathematica finds the solution is:
> t==82.9182
> 
> Where am I making an error? Is my hand calculation wrong, or is
> Mathematica wrong? Why am I getting an error message using Solve[] or
> NSolve[] with Mathematica?
> 
> Thanks,
> Heath


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