eq1 := $y = -26.21231979*z+15.42332896+13.22411533*e^{-.6786000000*x}$

eq2 := $y = -25.98077423*z+14.81943362+13.53858145*e^{-.6569000000*x}$

Comparing both equations, eliminating $y$

$-26.21231979*z+15.42332896+13.22411533*e^{-.6786000000*x}$ = $-25.98077423*z+14.81943362+13.53858145*e^{-.6569000000*x}$

Putting $z$= $0.5044$

$-26.21231979*(0.5044)+15.42332896+13.22411533*e^{-.6786000000*x} $= $ -25.98077423*(0.5044)+14.81943362+13.53858145*e^{-.6569000000*x}$

I cannot find $x$ value? I tried it in Maple as well. But it doesn't evaluate the value of $x$. Any other solution?

Edit : My main task is to calculate value of $x$ by putting any value of $z$ This is just an example


Why do you believe that there is a value of x that satisfies you equations when z=0.5044?

eq1 := y=-26.21231979*z+15.42332896+13.22411533*exp(-0.6786*x):
eq2 := y=-25.98077423*z+14.81943362+13.53858145*exp(-0.6569*x):
q := rhs(eq1)-rhs(eq2);
plot3d( [0,q], x=-0.001..0.001, z=0.4..1.4,view=-1..1,color=[red,blue] );
plot3d( [0,q], x=-10..10, z=0.4..1.4,view=-1..1,color=[red,blue] );
Optimization:-Minimize(z,{q<=0,q>=0},x=-0.001..0.001, z=1.1..1.3);

The surfaces computed by the above plot3d calls do not seem to fall below (or touch) height 0.0 unless z is at least some value greater than 1. Something above z=1.2496 or so. Do you have a reason to believe otherwise?

  • 1
    $\begingroup$ Nice observation. The bound $z=1.184210000$ can be found by differentiating both sides of the equation by $x$, solving for $x$, then substituting this back into the original equation and solving for $z$. $\endgroup$ – Antonio Vargas Dec 9 '13 at 6:53

In Maple, use the command fsolve. Remember to use exp(x) for $e^x$.

  • $\begingroup$ I tried this command as well $ fsolve(eval(rhs(eq1) = rhs(eq2), z = 0.5044)$ $\endgroup$ – Syeda Dec 9 '13 at 6:19
  • $\begingroup$ Did you use exp for $e$? $\endgroup$ – Carl Love Dec 9 '13 at 6:23
  • $\begingroup$ Yes. I input $exp$ as well $\endgroup$ – Syeda Dec 9 '13 at 6:27
  • 1
    $\begingroup$ Plotting leads me to believe, like Acer, that there is no solution for this $z$. $\endgroup$ – Carl Love Dec 9 '13 at 6:53
  • $\begingroup$ @Carl.. okay!! Thank you!! $\endgroup$ – Syeda Dec 9 '13 at 7:38

I suppose that the value you gave to "z" is wrong or that your coefficients are wrong. Using the numbers given in your post, there is no solution to your problem. In order to have a solution close to x=0.501, "z" should be of the order of 1.18421 (as reported by acer). The difference of your two equations goes to an extemum for x = 0.414684 and for this value this difference has a value equal to (-0.274199 + 0.231546 z).

  • $\begingroup$ okay!! I got it. I agree with acer.. I will put $z= 1.184221$. But my main issue is why this tool is not evaluating value of $x$ ?? $\endgroup$ – Syeda Dec 9 '13 at 7:02
  • 1
    $\begingroup$ @Syeda. If there is no solution to your equation, what do you want Maple to do ? $\endgroup$ – Claude Leibovici Dec 9 '13 at 7:31
  • $\begingroup$ @Claude.. okay!! Its means my approach is wrong! :( Thankyou.. $\endgroup$ – Syeda Dec 9 '13 at 7:35

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