1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding coefficients from equation

  1. Oct 15, 2008 #1
    I am stuck on a math problem for one of my engineering courses which seems fairly straight forward, but I have had little success with. The problem reads as follows:
    The following data has the form y=ax^b. Estimate the coefficients a+b.
    Given data:
    Y X
    1: (0.0014) (0.5)
    2: (0.0251) (2)
    3: (0.153) (5)
    4: (0.6371) (10)

    What I was trying to do was plug in the first set of values and solve the equation for one coefficient in terms of the other. Then I would take the second set of data and plug my answer in, giving me like terms. If someone could explain to me the process of solving this equation I would really appreciate it
  2. jcsd
  3. Oct 15, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Log y = Log a + b Log x

    Use least squares to estimate Log a and b.
  4. Oct 16, 2008 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    The problem does not ask you to FIND the coefficients, it asks you to ESTIMATE them. Putting x and y equal to each pair of given numbers into y= axb gives you an equation for a and b. You should only need two equations but you have four and probably can't find a single a and b that will satisfy all four.

    From the "extreme" pairs, 0.0014= a (0.5)b and .6731= a 10b. Dividing the second by the first eliminates a: .6731/.0014= 0.5b/10b which is the same as 480= (1/20)b= 20-b. As EnumaElish said, you will need to use logarithms to solve that.

    (Thanks to TheoMcCloskey for noting my error. I had started to use the first two points and didn't complete change when I decided to use first and last.)
    Last edited: Oct 16, 2008
  5. Oct 16, 2008 #4
    Hall's - I think you better review your response - it needs some corrections.
  6. Oct 16, 2008 #5
    Thank you for the help. I was able to determine the answer both algebraically and on my calculator
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?