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Math Help - prove this log

  1. #1
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    prove this log

    alright so the question is this:

    how do u prove this equation:

    log base b times M^k= K times log base b times M

    sorry about the writing of the equation, i dunno how to type mathmatically =p
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by abowlofrice
    alright so the question is this:

    how do u prove this equation:

    log base b times M^k= K times log base b times M

    sorry about the writing of the equation, i dunno how to type mathmatically =p
    Let a=log_b(M^k), then (assuming M is positive and k is real):

    b^a=M^k, (definition of log_b)

    so:

    b^a=(b^{log_b(M)})^k, (again using the definition of log_b).

    So:

    a=k.log_b(M), (using (u^v)^w=u^{v.w} and b^a=b^c implies a=c).

    Which is:

    log_b(M^k)=k.log_b(M).

    RonL
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  3. #3
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    thx man, made me one step closer to loving math.... =]
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