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Re: Help with factoring out an exponential
*To*: mathgroup at smc.vnet.net
*Subject*: [mg2320] Re: Help with factoring out an exponential
*From*: danl (Daniel Lichtblau)
*Date*: Tue, 24 Oct 1995 02:13:46 -0400
*Organization*: Wolfram Research, Inc.
In article <DGvx73.AxH at wri.com> Rob Carscadden
<carscadd at pps.pubpol.duke.edu> writes:
> I'm am trying to solve and equation but I can't factor out an
> exponential.
>
> I have an equation which will be given below, which has two
exponentials:
> after taking the dervivatives I want to factor these out (throw them
away
> really) so that mathematica has an algebraic equation to work with and I
> can find the critical points. Clearly these wil never be zero so I'm not
> losing anything.
> Here's my code where c is 5^x
>
> Print[eqn];
> tempeqn = D[eqn,x];
> test = Simplify[tempeqn/(Exp[-x^2/2])];
> eqn1 = Simplify[test/c];
> soln = Solve[eqn1 == 0,x]//N;
> Print[eqn1];
>
> and here's my results:
>
> 2
> x 0.75 0.09375 (1.5 + x)
> 5 (---------------- - ------------------)
> 2 2
> x /2 x /2
> E Sqrt[2 Pi] E Sqrt[2 Pi]
>
>
>
>
> x x x 2 x 3
> (0.09375 (-3. 5 - 7.75 5 x + 3. 5 x + 1. 5 x
>
> x
> + 5.75 5 Log[5] -
>
> x x 2 x
> 3. 5 x Log[5] - 1. 5 x Log[5])) / (5 Sqrt[2 Pi])
>
>
> As you can see every term in the numerator has an 5^x but it won't
cancel
> with the denominator. Why?
>
> I'm goin gback to mathematica and try a change of base formula and see
if
> this helps.
>
> Thanks for your help
>
Two things I would recommend.
(1) Print this using InputForm so others can cut-and-paste to try it out.
(2) Make everything exact. The presence of inexact numbers will reliably
cause Cancel et al to fail. There is a note to this effect in the
reference manual, section 3.3.4, bottom p. 597. It applies to the
functions described in the preceding section as well. This is of course a
defect in the documentation.
Daniel Lichtblau
Wolfram Research
danl at wri.com
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