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Math Help - A proof involving logs

  1. #1
    Junior Member
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    A proof involving logs

    Can anyone show that:

    .......................N-1
    log(N-1)! = \Sigman=1 log(n)

    NB: The dots leading up to the "N-1" on the top line are just to make it line up with the n=1 as it part of the summation bit and i couldnt work out how to do it using latex math!
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  2. #2
    Super Member Deadstar's Avatar
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    Quote Originally Posted by Mathman87 View Post
    Can anyone show that:

    .......................N-1
    log(N-1)! = \Sigman=1 log(n)

    NB: The dots leading up to the "N-1" on the top line are just to make it line up with the n=1 as it part of the summation bit and i couldnt work out how to do it using latex math!
    \log(n) + \log(m) = \log(mn)

    So \sum_{n=1}^{N-1} \log(n) = \log(1) + \log(2) + \log(3) + \dots + \log(N-1)

    = \log(1\cdot2\cdot3 \dots \cdot (N-1)) = \log((N-1)!)
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  3. #3
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    makes sense, thank you! :-)
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