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Math Help - f(6) = ?

  1. #1
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    f(6) = ?

    Sorry if this is wrong section, I'm not sure where else to post. I am stuck with this problem:

    f(x)= m * 2​kx
    where
    f(3)=27
    f(4)=36
    Question is: What is f(6)?


    I can't figure how to solve either k or m; or how to substitute either of them for something useful. According to my textbook the answer is 64, but I have no idea how to get there. Any help is appreciated.
    Last edited by keuko667; March 29th 2013 at 09:10 PM.
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  2. #2
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    Re: f(6) = ?

    You should end up with two equations:

    \displaystyle \begin{align*} 27 &= m\cdot 2^{3k} \\ 36 &= m \cdot 2^{4k} \end{align*}

    Do you see where these equations come from?

    To eliminate one of the variables, the easiest thing to do would be to divide the second equation by the first...
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  3. #3
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    Re: f(6) = ?

    Keuko667

    substitute x=4 first to the given relation and find : 36= m 2^(4k),
    then substitute again x= 3 and find 27 = m 2^(3k)
    divide these two equations and m disapears...you wil get 36/27=2^ k then get the logarithms of both sides to find the value of k .
    the last step is to substitute k in one of the two equations and solve it for m ... After all these you know the complete formula of the function substitute x= 6 and find all what you need. As simple as such... try it....

    MINOAS
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    Re: f(6) = ?

    Sorry Prove it....when I saw it your answer was not there...

    MINOAS
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  5. #5
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    Re: f(6) = ?

    I hadn't thought of dividing the pair, thank you very much for the help both!
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