Google Groups no longer supports new Usenet posts or subscriptions. Historical content remains viewable.
Dismiss
Exponential Equation - How do you solve this one please?
20 views
Skip to first unread message
JoeCL
May 17, 2013, 4:52:13 PM5/17/13
to
Hi Everyone,
I am challenged today by trying to find a solution to this equation. Am I
missing something, or is this a tough one. There is only one variable, W,
all the others are constants (C,D,E,F,G)
E = F*exp(CW) + G*exp(DW)
I'm seeking W=?
The only thought I had was taking the derivative with respect to W and
substituting it back into the equation but I'm not sure if that's a
mathematically sound way to solve this.
Any help would be much appreciated.
Thank you in advance,
Julian
:-)
I am challenged today by trying to find a solution to this equation. Am I
missing something, or is this a tough one. There is only one variable, W,
all the others are constants (C,D,E,F,G)
E = F*exp(CW) + G*exp(DW)
I'm seeking W=?
The only thought I had was taking the derivative with respect to W and
substituting it back into the equation but I'm not sure if that's a
mathematically sound way to solve this.
Any help would be much appreciated.
Thank you in advance,
Julian
:-)
Virgil
May 17, 2013, 6:15:50 PM5/17/13
to
In article <IYmdnVRo2L_iBQvM...@earthlink.com>,
If you have numerical values for all of C,D,E,F and G, you might be able
to find an approximate numeric solution for W, but unless C = D or both
C and D are both very small integers like 1 and 2, an exact general
solution seems unlikely.
--
to find an approximate numeric solution for W, but unless C = D or both
C and D are both very small integers like 1 and 2, an exact general
solution seems unlikely.
--
AMiews
May 17, 2013, 7:43:50 PM5/17/13
to
"JoeCL" <jo...@earthlink.net> wrote in message
news:IYmdnVRo2L_iBQvM...@earthlink.com...
> Hi Everyone,
>
> I am challenged today by trying to find a solution to this equation. Am I
> missing something, or is this a tough one. There is only one variable, W,
> all the others are constants (C,D,E,F,G)
>
> E = F*exp(CW) + G*exp(DW)
>
> I'm seeking W=?
>
E = exp(W) * ( F * exp(C) + G * exp(D) )
>
> I am challenged today by trying to find a solution to this equation. Am I
> missing something, or is this a tough one. There is only one variable, W,
> all the others are constants (C,D,E,F,G)
>
> E = F*exp(CW) + G*exp(DW)
>
> I'm seeking W=?
>
exp (W) = E / ( F * exp(C) + G* exp(D) )
W = Ln ( E / ( F * exp(C) + G* exp(D) ))
so........ wheres the beef ?
sanebow
May 17, 2013, 7:57:53 PM5/17/13
to
"AMiews" <inv...@invalid.com> wrote in message
news:kn6fbu$ode$1...@news.albasani.net...
JoeCL
May 17, 2013, 8:01:24 PM5/17/13
to
exp(CW) = (exp(c))^W = (exp(W))^C
You're treating exp(CW) as exp(c) * exp(W) and that's not right.
exp(c+w) = exp(c) * exp(w)
Very best,
Julian
JoeCL
May 17, 2013, 8:03:29 PM5/17/13
to
"Virgil" <vir...@ligriv.com> wrote in message
news:virgil-82E74C....@BIGNEWS.USENETMONSTER.COM...
This is what I suspected, but thought I was missing something obvious. I
either need an exact solution or will have to abandon this approach.
Most appreciatively,
Julian
:-)
Ken Pledger
May 19, 2013, 6:52:33 PM5/19/13
to
In article <virgil-82E74C....@BIGNEWS.USENETMONSTER.COM>,
polynomial equation which may not be too bad to solve. For example, if
C/D = 2, then let x = exp(DW) to get the quadratic equation
F(x^2) + Gx = E.
But if C/D is nastier, then you will need a numerical approach as Virgil
mentioned. I would let x = exp(DW) and then try Newton-Raphson, but
there may be better ways.
Ken Pledger.
Virgil <vir...@ligriv.com> wrote:
> In article <IYmdnVRo2L_iBQvM...@earthlink.com>,
> "JoeCL" <jo...@earthlink.net> wrote:
>
> > .... There is only one variable, W,
> In article <IYmdnVRo2L_iBQvM...@earthlink.com>,
> "JoeCL" <jo...@earthlink.net> wrote:
>
> > all the others are constants (C,D,E,F,G)
> >
> > E = F*exp(CW) + G*exp(DW)
> >
> > I'm seeking W=?
> > ....
> >
> > E = F*exp(CW) + G*exp(DW)
> >
> > I'm seeking W=?
>
> If you have numerical values for all of C,D,E,F and G, you might be able
> to find an approximate numeric solution for W, but unless C = D or both
> C and D are both very small integers like 1 and 2, an exact general
> solution seems unlikely.
If either C/D or D/C is a small natural number, then you have a
> If you have numerical values for all of C,D,E,F and G, you might be able
> to find an approximate numeric solution for W, but unless C = D or both
> C and D are both very small integers like 1 and 2, an exact general
> solution seems unlikely.
polynomial equation which may not be too bad to solve. For example, if
C/D = 2, then let x = exp(DW) to get the quadratic equation
F(x^2) + Gx = E.
But if C/D is nastier, then you will need a numerical approach as Virgil
mentioned. I would let x = exp(DW) and then try Newton-Raphson, but
there may be better ways.
Ken Pledger.
JoeCL
May 20, 2013, 1:18:39 AM5/20/13
to
"Ken Pledger" <ken.p...@vuw.ac.nz> wrote in message
news:ken.pledger-F23D...@news.eternal-september.org...
Yes, unfortunately the C & D are not so convenient.
I gave some serious consideration to treating W, C, and D as complex numbers
such that the real part would come out as expected, an the imaginary parts
would allow manipulation, but I have no concrete solution and perhaps my
ability to manipulating complex numbers was just not up to the task. I ended
up with more variables than I started with and no clear direction to
resolving them. Still, it seems complex number treatment might have a
solution in there somewhere.
I appreciate your time and thoughts.
Many blessings,
Julian
:-)
0 new messages