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Math Help - Taking ln of both sides

  1. #1
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    Taking ln of both sides

    I need to change y = 1.378x^-.654

    and plot it as lny vs lnx

    The question says plot the points x=10, 20, 30...100 for the original y=mx+b function. I've done that but I'm not sure how I'd convert it so that it's in the form of lny = lnx + b for the values x=10, 20, 30...100
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  2. #2
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    Quote Originally Posted by SportfreundeKeaneKent View Post
    I need to change y = 1.378x^-.654

    and plot it as lny vs lnx

    The question says plot the points x=10, 20, 30...100 for the original y=mx+b function. I've done that but I'm not sure how I'd convert it so that it's in the form of lny = lnx + b for the values x=10, 20, 30...100
    Well,
    y = 1.378x^{-0.654}

    ln(y) = ln \left ( 1.378x^{-0.654} \right )

    ln(y) = ln(1.378) + ln \left ( x^{0.654} \right )

    ln(y) = ln(1.378) + 0.654 ln(x)

    ln(y) = 0.654 ln(x) + ln(1.378)

    So the equation is a line on the log-log plot with a slope of 0.654 and an intercept (where x = 1 not x = 0!) of ln(1.278).

    -Dan
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  3. #3
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    Iím still having problems with this. I can derive the equation like you have but Iím unsure of how to graph it on excel or something. When I plug in the values of 10,20,30Ö100 for x, the graph I get is curved. How would I plot it on a log log plot in excel to get a straight line?
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by SportfreundeKeaneKent View Post
    Iím still having problems with this. I can derive the equation like you have but Iím unsure of how to graph it on excel or something. When I plug in the values of 10,20,30Ö100 for x, the graph I get is curved. How would I plot it on a log log plot in excel to get a straight line?
    Write out an Excel spreadsheet like this:
    The top columns are going to be x, y, log(x), and log(y). Put your x, y data down the x, y columns, then calculate the log(x) and log(y) for each data point. Now make a graph with log(x) for the x data and log(y) for the y data.

    -Dan
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