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Homework Help: I need help changing an equation

  1. Feb 12, 2010 #1
    1. The problem statement, all variables and given/known data
    So, I'm given the equation T = kL^3/2

    Data: L= .9, .8, .7, .6, .5 and T=.558, .47, .375, .323, .26 (.9 goes with .558, etc)

    I need to find the constant k by changing T=kL^3/2 into log form

    2. Relevant equations

    3. The attempt at a solution
    Last edited: Feb 12, 2010
  2. jcsd
  3. Feb 12, 2010 #2
    "Rewriting the equation in log form" essentially means to take logarithms on both sides of the equation. So, we obtain
    [tex]log T = log (k\,L^{\frac{3}{2}})[/tex]​

    I'm sure you can go on in further simplifying the expression?
  4. Feb 12, 2010 #3
    Well, I see you've edited your post with the data.
    To solve for k, what we are doing here is actually linearising the relation between T and L so that we can plot a nice straight line.
    Simplifying the expression further, we get:
    [tex]log\,T = log\,k + \frac{3}{2}log\,L[/tex]​

    Clearly, plotting log T against log L (values obtained from your data) will yield a gradient of 3/2 and a y-intercept of log k. This enables you to obtain the value of k.
  5. Feb 12, 2010 #4
    how does making the relation linear allow me to find k?
  6. Feb 12, 2010 #5
    It allows you to plot a simple straight line graph in the form y = mx + c from which you can extract information from.
    As I mentioned in my earlier post, plotting y (log T) against x (log L) will yield a gradient m (3/2) and a y-intercept c (log k). Obtain the y-intercept value from the graph, which is equal to log k, and solve from k from there.
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