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Thread: Logs proofs

  1. #1
    May 2007

    Logs proofs

    I have a couple of properties that need to be proven.

    Use the definition a^x = e^(x log a) to derive the following properties of general exponentials:

    a) (ab)^x = (a^x)(b^x)

    b) (a^x)(a^y) = a^(x+y)

    c) (a^x)^y = (a^y)^x = a^(xy)

    Thank you
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  2. #2
    Junior Member
    Dec 2006
    (ab)^x=e^(xlogab)=e^(x*(loga+logb))=e^(xloga+xlogb )=e^(xloga)*e^(xlogb)=a^x*b^x
    Hope this gives you a hint how to do the other ones.
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