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I An exponential number algebra problem

  1. Mar 17, 2019 at 4:38 AM #1
    Let a,b,c and n are real numbers.


    a-b = C
    I want to get rid of a,b and find the following expression in terms of C and n. How can I do that?
    (an-bn)= ? (in terms of C and n)

    Thank you.
     
  2. jcsd
  3. Mar 17, 2019 at 4:51 AM #2

    mfb

    Staff: Mentor

    You can't.
    Simple example: a=2, b=1 and a=1, b=0 both lead to C=1, but a2-b2 is different for the two cases.

    You can rewrite an-bn to have a factor of (a-b) but you won't get rid of a and b completely.

    What is the context of this question?
     
  4. Mar 17, 2019 at 5:01 AM #3
    I have a resonator and the resonance frequency (w) of it is given by w=A(L-1.5) where A is a constant and L is the length. When I apply a force the resonance frequency changes because length of the beam changes due to deformation. I need to find the change in resonance frequency as a function of change in length.



    That's why I said winitial = ALinitial-1.5
    and ALfinal-1.5
    Lfinal-Linitial = (Linitial.Ftensile)/(EAcrossection)
    Where E is the young modulus and A is the area.
    In my question a and b were Linitial and Lfinal
    n was -1.5
    C was (Linitial.Ftensile)/(EAcrossection)
     
    Last edited: Mar 17, 2019 at 5:12 AM
  5. Mar 17, 2019 at 5:05 AM #4

    BvU

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    So where are the ##a## and ##b## in your story ?
     
  6. Mar 17, 2019 at 5:11 AM #5
    In my question a and b were Linitial and Lfinal
     
  7. Mar 17, 2019 at 5:15 AM #6

    BvU

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    So take logarithms ! $$\ln\omega = \ln A - 1.5\ln L$$
     
  8. Mar 17, 2019 at 5:17 AM #7
    I will try thanks
     
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