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MathGroup Archive 1995

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Help with factoring out an exponential

  • To: mathgroup at smc.vnet.net
  • Subject: [mg2304] Help with factoring out an exponential
  • From: Rob Carscadden <carscadd at pps.pubpol.duke.edu>
  • Date: Mon, 23 Oct 1995 12:42:58 -0400
  • Organization: Duke University, Durham, NC, USA

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



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