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Math Help - log problem

  1. #1
    Newbie
    Joined
    Feb 2007
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    5

    log problem

    How does the following log transformation work?

    (3/2)^(log2 n) = (2)^((log2 n)(log2 3/2))

    I think I'm just missing something little here, but I can't think of what...

    Sorry about the math, I couldn't get the math tags to work.
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  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
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    Hello, jtc4zH!

    There may be other ways . . . possibly simpler.


    How does the following log transformation work?

    \left(\frac{3}{2}\right)^{\log_2(n)} \;=\;2^{\log_2(n)\cdot\log_2(\frac{3}{2})}
    \text{Let: }\;x \;=\;\left(\frac{3}{2}\right)^{\log_2(n)}


    \text{Take logs (base 2): }\;\log_2(x) \;=\;\log_2\!\left(\frac{3}{2}\right)^{\log_2(n)} \;=\;\log_2(n)\cdot \log_2\!\left(\frac{3}{2}\right)


    \text{Exponentiate: }\;\underbrace{2^{\log_2(x)}}_{\text{This is }x} \;=\;2^{\log_2(n)\cdot\log_2(\frac{3}{2})}


    \text{Therefore: }\;\left(\frac{3}{2}\right)^{\log_2(n)} \;=\;2^{\log_2(n)\cdot\log_2(\frac{3}{2})}

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