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Homework Help: 2^(-log2(x)) log

  1. May 22, 2004 #1
    2^(-log2(x)) It reads, 2 to the power of -log base2 x

    The problem is that I don't understand why this can also be written as x^-1

    For some reason the base and the log2 cancel out. Can anyone explain to me why this happens, please?

    1/2^(log2(x)) = 1/x
     
  2. jcsd
  3. May 22, 2004 #2

    arildno

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    -log2(x)=log2(x^(-1)),
    by the rule for logarithms:
    blog(a)=log(a^(b))
     
  4. May 22, 2004 #3

    Zurtex

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    Or you could use that:

    [tex]a^{bc} = \left(a^c \right)^b[/tex]

    As [itex]- \log_2 x = (-1) \log_2 x[/itex]
     
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