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Math Help - Logarithm Proof

  1. #1
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    Question Logarithm Proof

    How do I prove that a^(log x with the base of a) = x? All I know is that it does equal x.
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  2. #2
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    Quote Originally Posted by xwrathbringerx View Post
    How do I prove that a^(log x with the base of a) = x? All I know is that it does equal x.
    The logarithm function, let's call it g(x),  g(x) = \log_{a} x, is defined as the inverse function of f(x) = a^x.

    From the definition of an inverse function we know if must be true that
    f(f^{-1}(x))=x

    So applying that definition here

    f(g(x)) = x
    f(\log_{a} x) = x
    a^{\log_{a} x} = x

    And there you have it.
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