Solving Equation Ʃ(ai^x -b)^2 = C

[Mikca10]

Hi,

I want to solve the following equation by x:



Ʃ(ai^x -b)^2 = C ,
where Ʃ is over all i, i = 1:N, and ^ means "to the power of"

How to find x from here?

Thanks!

 

[berkeman]

Hi,

I want to solve the following equation by x:



Ʃ(ai^x -b)^2 = C ,
where Ʃ is over all i, i = 1:N, and ^ means "to the power of"

How to find x from here?

Thanks!

Welcome to the PF.

What is the context of the question? Is it from schoolwork?

 

[alexfloo]

Try expanding the quadratic that's in the sum. Then you should ultimately be able to turn it into one quadratic equation.

 

[AlephZero]

Try expanding the quadratic that's in the sum.

It isn't a quadratic. The equation is \sum(a_i^x -b)^2 = C , not \sum(a_ix -b)^2 = C

 

[alexfloo]

Ah my mistake. Thanks a lot.

 

[Mikca10]

it is not the homework, it's more like a part of a research problem.. my algebra class was long time ago.

 

[Mikca10]

Anyone has a clue?

 

[alexfloo]

If you want an analytical solution for the general case, I'd say (pretty confidently) that it just can't be done. If you have specific values for the a_i, then I'd try it numerically.