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