# Math Help - Product problem.

1. ## Product problem.

How do I find the following?

$\prod a(1-x_{i})^{a-1}$?

I assume it's $a^n$ multiplied by something. I can't figure out how to express the product of the $(1-x_{i})^{a-1}$ part.

2. Originally Posted by Zenter
How do I find the following?

$\prod a(1-x_{i})^{a-1}$?

I assume it's $a^n$ multiplied by something. I can't figure out how to express the product of the $(1-x_{i})^{a-1}$ part.
Is the problem to "simplify" $\prod\limits_{i=1}^n a(1-x_{i})^{a-1}$? If so, not much can be done: since the $x_i$ dependence on the product index $i$ is not known. But maybe you are already happy with something like this
$\prod\limits_{i=1}^n a(1-x_{i})^{a-1}=a^n \left(\prod\limits_{i=1}^n(1-x_i)\right)^{a-1}$

3. Well, I need to "simplify" it so I'm able to get the log of it.

Or is there a way to get the log of it in that form?

4. Originally Posted by Zenter
Well, I need to "simplify" it so I'm able to get the log of it.

Or is there a way to get the log of it in that form?
Sure, like this

$\log\left(a^n\left(\prod\limits_{i=1}^n(1-x_i)\right)^{a-1}\right)=n\log(a)+(a-1)\sum\limits_{i=1}^n\log(1-x_i)$

5. Oh! Brilliant, thank you