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I forgot how to solve for an exponent

  1. Jan 15, 2009 #1
    1. The problem statement, all variables and given/known data
    i need to solve for b in f(x)=a*xb
    i know f(1.5)=10 and f(1.7)=14

    it's been forever since i did calc like this and i am blank on what to do.
    i can't remember if or how i can set them equal to each other to solve for b.
    i know i have 2 eqns and 2 unknowns.

    do i set f(1.5)=f(1.7)? i don't think that's right but i can't think of what else to do??
  2. jcsd
  3. Jan 15, 2009 #2
    Why would you set them equal to each other? You know they equal 10 and 14 respectively so are you saying 10 = 14?

    What you should do is plug it in, i.e. f(1.5) = a*1.5^b = 10 then do the same with the other point, now you will have 2 equations and 2 unknowns, so for example a = 10/1.5^b, figure out what a = in the other equation and set THOSE equal to each other.
  4. Jan 15, 2009 #3
    alright i'm an idiot.
    so you get something like 14/10=(1.7/1.5)^b and then take natural log of each side right...?
  5. Jan 15, 2009 #4
    Assuming your algebra is correct, yes.
  6. Jan 15, 2009 #5
    sweet thanks a lot
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