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MathGroup Archive 1999

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Solving equations involving Ln function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19851] Solving equations involving Ln function
  • From: Satyajit Bose <sgb2 at columbia.edu>
  • Date: Sun, 19 Sep 1999 01:20:35 -0400
  • Organization: Columbia University
  • Sender: owner-wri-mathgroup at wolfram.com

Hello,

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
my input line and results in the kernel:

In[1]:=
Solve[Log[x]+delta*v==Log[(1-delta)*x/(1-delta^2)]+delta*Log[(1-delta)*d

elta*x/(1-delta^2)]+delta^2*v,x]

Solve::tdep: The equations appear to involve transcendental functions of
the
    variables in an essentially non-algebraic way.

Out[1]= Solve[delta v + Log[x] ==

           2         (1 - delta) x              (1 - delta) delta x
>     delta  v + Log[-------------] + delta Log[-------------------], x]

                               2                             2
                      1 - delta                     1 - delta

I am hoping to get a solution that looks like this:

x -> exp[v*(1-delta)]*(1+delta)^(1+1/delta)/delta)

Thank you for all your  help.

Sayajit Bose
--
Satyajit Bose
Department of Economics                    New York, NY 10027
Columbia University                        (212) 665-8208
http://www.columbia.edu/~sgb2              sgb2 at columbia.edu




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