       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 -
>
>          x                   x      2                  x
>   3.   5  x Log - 1.    5      x  Log))   /   (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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