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    ???????
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    Rearranging D, you get  \log y =\log a +b\log x . So if you plot log x against log y, it will be a straight line as the equation will have a linear form,  Y=mX+c , where  m=b, X=\log x, Y=\log y and  c=\log a .
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    (Original post by RLJCMorrissey)
    ???????
    Because D is the only one that provides a linear relationship when log(y) is plotted against log(x).

    y=ax^b \rightarrow log(y)=log(ax^b) \rightarrow log(y)=log(a)+log(x^b) \rightarrow log(y)=log(a)+blog(x)

    ...which is in the form y=mx+c as a and b are constants and y\mapsto log(y), x\mapsto log(x), c\mapsto log(a)
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    @B_9710 Hmm, I did think that was the case but surely having logs in there means it doesn't quite come out as a straight line?
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    (Original post by RLJCMorrissey)
    @B_9710 Hmm, I did think that was the case but surely having logs in there means it doesn't quite come out as a straight line?
    No, it will be a perfect straight line as you are plotting log y against log x. If you had log y =x , by plotting log y against log x you would plot a straight line. That is kind of the point, it's much easier to work with straight lines than curves.
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    (Original post by RLJCMorrissey)
    @B_9710 Hmm, I did think that was the case but surely having logs in there means it doesn't quite come out as a straight line?
    Why? Anything that can be rearranged to y=mx+c is a straight line. If you can't convince yourself try plotting it
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    I just can't quite get my head around why those logs won't cause it to curve : s
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    (Original post by RLJCMorrissey)
    I just can't quite get my head around why those logs won't cause it to curve : s
    You are plotting a graph of the form Y = mX + c, with Y on the vertical axis and X on the horizontal axis. The fact that Y and X can be expressed as logarithms of other variables is irrelevant, the point is that they are variable and continuous (well, by continuous in this context I am saying that over a certain interval they take every single real value)
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    (Original post by RLJCMorrissey)
    I just can't quite get my head around why those logs won't cause it to curve : s
    Well, because the logs are on the axis you're not really plotting them. Try thinking about it in terms of another two variables.
    p=log x and q=log y
    so you're now plotting
    q=log a + bp
    Since log a is a constant this is clearly a straight line- it just so happens that q and p are linked to x and y using logs. They can still take any value.
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    (Original post by sindyscape62)
    Well, because the logs are on the axis you're not really plotting them. Try thinking about it in terms of another two variables.
    p=log x and q=log y
    so you're now plotting
    q=log a + bp
    Since log a is a constant this is clearly a straight line- it just so happens that q and p are linked to x and y using logs. They can still take any value.
    Ahhh got it now.

    Thanks a lot!
 
 
 
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