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From: spiceman on 23 Jul 2010 07:08
Hi everybody,

does anybody have a clue how to get Mathematica to deliver the inverse of the following function?

fct := c + (k * Log[x]) + (d - c)/(1 + Exp[b*(Log[x] - Log[e])])^f
Solve[fct == y, x]

Solve::tdep: The equations appear to involve the variables to be solved for in an essentially non-algebraic way.

I suppose I have to transform somehow. Any clues?
Omitting k*Log[x] works...

Thnaks in advance,
-ans

From: Bill Rowe on 24 Jul 2010 05:06
On 7/23/10 at 7:08 AM, aspiess(a)uke.de (spiceman) wrote:

>does anybody have a clue how to get Mathematica to deliver the
>inverse of the following function?

>fct := c + (k * Log[x]) + (d - c)/(1 + Exp[b*(Log[x] - Log[e])])^f
>Solve[fct == y, x]

>Solve::tdep: The equations appear to involve the variables to be
>solved for in an essentially non-algebraic way.

>I suppose I have to transform somehow. Any clues? Omitting k*Log[x]
>works...

Your expression has the form k*Log[x]+ p[x] where p is a
polynomial. Deleting the k*Log[x] makes your expression a
polynomial which Solve can deal with. Leaving the k*Log[x] in
makes it so that there is no closed form general solution. The
only way to solve this is to insert specific numeric values for
the coefficients and use one of the various numeric routines in
Mathematica such as FindRoot to get a numeric solution for x.


From: J. Batista on 24 Jul 2010 05:08
If I understood the statement of your problem correctly, omitting the term
k*Log[x] works merely because the mathematical expression is then no longer
implicit. Therefore, using your original mathematical expression, it does
not look like you are going to be able to generate x = f(y) from y = f(x) in
this case. Your original y = f(x) is an implicit function.

Regards,
J. Batista



On Fri, Jul 23, 2010 at 7:08 AM, spiceman <aspiess(a)uke.de> wrote:

> Hi everybody,
>
> does anybody have a clue how to get Mathematica to deliver the inverse of
> the following function?
>
> fct := c + (k * Log[x]) + (d - c)/(1 + Exp[b*(Log[x] - Log[e])])^f
> Solve[fct == y, x]
>
> Solve::tdep: The equations appear to involve the variables to be solved for
> in an essentially non-algebraic way.
>
> I suppose I have to transform somehow. Any clues?
> Omitting k*Log[x] works...
>
> Thnaks in advance,
> -ans
>
>
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