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Thread: 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 $\displaystyle a=log_b(M^k)$, then (assuming $\displaystyle M$ is positive and $\displaystyle k$ is real):

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

    so:

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

    So:

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

    Which is:

    $\displaystyle log_b(M^k)=k.log_b(M)$.

    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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