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Math Help - Logarithm Help

  1. #1
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    Logarithm Help

    If \log_{10} (x - 2) - 3 \log_{10} (2x) = 1 - \log_{10} (y), then y is equal to
    Last edited by mr fantastic; September 13th 2009 at 03:59 AM. Reason: Fixed latex
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  2. #2
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    Quote Originally Posted by user_5 View Post
    If \log_{10} (x - 2) - 3 \log_{10} (2x) = 1 - \log_{10} (y), then y is equal to
    Using basic log rules:

    The left hand hand side can be written \log_{10} \frac{x - 2}{8x^3}.

    The right hand side can be written \log_{10} 10 - \log_{10} y = \log_{10} \frac{10}{y}.

    Therefore ....
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  3. #3
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    Oh, thanks I forgot that 1 can be rewritten like that.
    It makes sense now.

    Is the answer is  y= \frac {80x^3}{x-2} ?
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  4. #4
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    Yes, well done

    But don't forget the restrictions on X, for the equation to produce a positive number (necessary for a log).

    x>2 and x<0
    Last edited by Finley; September 13th 2009 at 05:11 AM.
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