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Math Help - Logarithmics

  1. #1
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    Logarithmics

    How would I solve:

    2log n - log 2n = 2
    3 3

    and the 3's should be under that logs right side.
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  2. #2
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    Quote Originally Posted by Stuart
    How would I solve:

    2log n - log 2n = 2
    3 3

    and the 3's should be under that logs right side.
    2\log_3 n-\log_3(2n)=2
    Thus, since 2\log_3 n=\log_3 n^2
    \log_3 n^2-\log_3 (2n)=2
    The quotient rule,
    \log_3\left(\frac{n^2}{2n}\right)=2
    Cancel out the n's,
    \log_3\left(\frac{n}{2}\right)=2
    By the definition of logs,
    \frac{n}{2}=3^2
    Thus,
    n=18
    Q.E.D.
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