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Math Help - Product problem.

  1. #1
    Junior Member
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    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.
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by Zenter View Post
    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}
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  3. #3
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    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?
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  4. #4
    Super Member Failure's Avatar
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    Quote Originally Posted by Zenter View Post
    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)
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  5. #5
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    Oh! Brilliant, thank you
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