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    Can anyone explain how this question is done:

    The points (2, 6) and (3, 18) lie on the curve y=ax^n
    Use logarithms to find the values of a and n, giving your answers correct to 2 decimal places.

    Many thanks in advance
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    Have you tried forming a system of two simultaneous equations in terms of a and n?

    (Hint: The points (2,6) and (3,18) lie on the curve, so you can try substituting them in as the x and y co-ordinates)
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    (Original post by Jarred)
    Have you tried forming a system of two simultaneous equations in terms of a and n?

    (Hint: The points (2,6) and (3,18) lie on the curve, so you can try substituting them in as the x and y co-ordinates)
    I have tried - but not succeeded.
    I ended up with something like (nlog18 = log3 - loga) - (nlog6 = log2 - loga) but didnt know how to progress further than that. I get log2 = log(3/2) ... which makes no sense what so ever
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    You have to graph logY again LogX

    x 2 3
    y 6 18
    logx 0.30103 0.4771
    logy 0.7782 1.2553

    You turn y=ax^n into a leaner form using logs:
    y = m*x + c
    logy = n*logx + loga

    Find the gradient to find n, find the y intercept to find a.
    Hope this helps
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    (Original post by KanKan)
    I have tried - but not succeeded.
    I ended up with something like (nlog18 = log3 - loga) - (nlog6 = log2 - loga) but didnt know how to progress further than that. I get log2 = log(3/2) ... which makes no sense what so ever
    How do you get that? Subtracting your 2 equations should give you your value for n.
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    (Original post by KanKan)
    I have tried - but not succeeded.
    I ended up with something like (nlog18 = log3 - loga) - (nlog6 = log2 - loga) but didnt know how to progress further than that. I get log2 = log(3/2) ... which makes no sense what so ever
    Here are the equations I got:

    log(6) = log(a)  +  n log(2)
    log(18) = log(a)  +  n log(3)

    From here, you just need to use the normal method of elimination. If you minus one equation from the other, you get rid of the log(a) term and can rearrange to find n.
 
 
 
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