How solve
08-08-2017, 03:48 AM
Post: #1
 yingwuluo Junior Member Posts: 32 Joined: Aug 2017
How solve
1-x*2.72^(-50*y)=100/z
1-x*2.72^(-100*y)=150/z
1-x*2.72^(-150*y)=250/z
08-08-2017, 03:05 PM
Post: #2
 ettlz Junior Member Posts: 20 Joined: Aug 2014
RE: How solve
With a pen and paper? $$x=-\frac12$$, $$y=-\frac{\log_{2.72}2}{50}$$, $$z=50$$
08-08-2017, 03:10 PM
Post: #3
 Helge Gabert Senior Member Posts: 467 Joined: Dec 2013
RE: How solve
Starting values? Any ideas what the feasible solution space should look like?

Using fsolve(), with blind values x=-.1, y=-.1,z=.1*i, I get [-.5, -1.38 . . .E-2, 50].
08-09-2017, 01:52 AM
Post: #4
 AlexFekken Member Posts: 151 Joined: May 2016
RE: How solve
(08-08-2017 03:05 PM)ettlz Wrote:  With a pen and paper? $$x=-\frac12$$, $$y=-\frac{\log_{2.72}2}{50}$$, $$z=50$$

Yes!

Really sad that somebody would even try a calculator or computer for a problem like this.
08-09-2017, 03:26 AM
Post: #5
 yingwuluo Junior Member Posts: 32 Joined: Aug 2017
RE: How solve
solve([1-x*e^(?50*y)=100/z,1-x*e^(?100*y)=200/z,1-x*e^(?150*y)=250/z],[x,y,z])
[/b]
["[y,e^(-50*y),e^(-100*y),e^(-150*y)] is not rational w.r.t. y Erreur: Valeur Argument Incorrecte"]

fsolve([(1-x*e^(-50*y)) = (100/z),(1-x*e^(-100*y)) = (200/z),(1-x*e^(-150*y)) = (250/z)],[x,y,z],[-0.1,-0.1,-0.1*i])

undef

Above output is the result from HP Prime Graphing Calculator, something wrong with it, please help me check if there is any input mistake.
08-09-2017, 05:52 AM
Post: #6
 parisse Senior Member Posts: 1,272 Joined: Dec 2013
RE: How solve
You can help solve by rewriting the system as a rational system
Code:
solve([(1-x*t) = (100/z),(1-x*t^2) = (150/z),(1-x*t^3) = (250/z)],[x,t,z])
then
Code:
solve(e^(-50*y)=t,y)
fsolve also works with a real starting point
Code:
fsolve([(1-x*e^(-50*y)) = (100/z),(1-x*e^(-100*y)) = (150/z),(1-x*e^(-150*y)) = (250/z)],[x,y,z],[-0.1,-0.1,0.1])
08-09-2017, 09:14 AM
Post: #7
 yingwuluo Junior Member Posts: 32 Joined: Aug 2017
RE: How solve
i tried to input i in solve symbolic view，it shows that irror：invalid input，please help me fix this problem.
08-09-2017, 01:58 PM (This post was last modified: 08-09-2017 01:59 PM by Helge Gabert.)
Post: #8
 Helge Gabert Senior Member Posts: 467 Joined: Dec 2013
RE: How solve
You didn't use the starting values I mentioned in my above post.

[-.1,-.1,.1*i]

Works for me.
08-09-2017, 03:03 PM
Post: #9
 yingwuluo Junior Member Posts: 32 Joined: Aug 2017
RE: How solve
What are the theory for using this starting value.
i tried to input i in solve symbolic view，it shows that irror：invalid input，please help me fix this problem.
08-09-2017, 04:00 PM
Post: #10
 Arno K Senior Member Posts: 469 Joined: Mar 2015
RE: How solve
I, as well as the others, I think, have not tried it in the solver-app. Switch to the command-line, I tried it in CAS, and the above mentioned entry beginning with fsolve(...) will do the job.
Arno
08-09-2017, 09:34 PM
Post: #11
 yingwuluo Junior Member Posts: 32 Joined: Aug 2017
RE: How solve
Thank you all. The members here are very active in solving the problem.
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