       Help with factoring out an exponential

• To: mathgroup at smc.vnet.net
• Subject: [mg2304] Help with factoring out an exponential
• 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 -

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.