Solving for x with A, b, and c Given

[Toby_Obie]

Hello,

Im trying to rearrange to find x from the below (all other values, A, b and c known)

$$A = bx / 1-(1+x)^-c$$

Below denominator ending reads (1+x)^(-c)

I've rearranged but to no avail, I'm unsure how to isolate x

Any input much appreciated

Thanks

 

[tiny-tim]

Hello Toby!

(you needed to put the index in curly brackets, {-c}, since it had more than one character … alternatively, try using the X² tag just above the Reply box )

This is the same as (1 + x)^-c = 1 - (b/A)x …

I don't think there is a "simple" solution.

But why are you looking for one?

 

[Toby_Obie]

Noted

I've never come up against an equation like this before, just curious whether it can be solved for x ? (new skills)

Is there a general solution to this type of equation ?

Can you point me in the right direction ?

Thanks very much

 

[tiny-tim]

Is there a general solution to this type of equation ?

I don't think so.

Real life just isn't that convenient!

 

[Toby_Obie]

Thanks anyway

Anybody else think they know the answer ?

 

[Mentallic]

Really, the problem is very complicated to solve, and for most $c\geq 4$ it's likely impossible to solve!

There is a proof that says for polynomials of degree 5 or higher, there is no way to solve the equation in its general case like quartics and below have been.

 

[Toby_Obie]

Okay

I'm using Excel to approximate x for known values of A, b, c

Thanks anyways

 

[Toby_Obie]

Just a note

Excel Goal Seek function solved my function to 4 decimal places, good tool