How to rewrite an infinite product of a production function.

Hi! Well I've been struggling with this equation (production function):

$\displaystyle \prod_{i=1}^n x_i^{a_i} = f(x) = y$

I need to find Xi in order to subtitute it in the equation (because I have to find the "cost function" of that production function) (pd: I've concluded that the following is the "cost function" i need to minimize):

$\displaystyle g(y,w) = \sum_{i=1}^n w_i x_i $

So I need to know how to deal with the product.

Thanks for your answers.

Re: How to rewrite an infinite product of a production function.

Hey Alm22.

Have you considered the log of f(x) or log(y)?

Minimizing the log of something is equivalent to minimizing that something.