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How do you determine wavelength, x, from this expresstion?

  1. Feb 14, 2009 #1
    1. The problem statement, all variables and given/known data

    The problem is a semiconductor question which I have resolved and gotten the equation:

    w = (50.12 x) ^ 0.5

    From the knowledge of this system, x is in an interval such that 0.5 < x < 2.5

    What mathematical method of solution would help find the solution to this equation? The value of x is supposed to be the minimum practical value for the solution.

  2. jcsd
  3. Feb 14, 2009 #2


    Staff: Mentor

    Square both sides.
  4. Feb 14, 2009 #3


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    Science Advisor

    You solve an equation by "backing out". Since the last thing done or the right was "0.5 power", which is the same as square root, so the opposite: square both sides. Then you are left with just 50.12x on the right. Since x is multiplied by 50.12, do the opposite: divide both sides by 50.12.
  5. Feb 14, 2009 #4
    Thanks for your ideas so far.

    Well, by squaring it and/or dividing it by 50.12, I am not going to be able to obtain the value of x still which should be in the interval 0.5 < x < 2.5 (from the theory of the physical problem).

    The value of w is unknown and the only way of finding it is by solving for this equation.

    Thanks again.
  6. Feb 14, 2009 #5


    Staff: Mentor

    Apparently you want to find the interval for w if 0.5 < x < 2.5 in this function:
    w = (50.12 x) ^ 0.5

    I interpreted your original post as wanting to find x.

    The function above is an increasing function, meaning that as x increases, so does w. On the interval 0.5 < x < 2.5, the smallest value of w will be for x = 0.5; the largest value for w will be for x = 2.5.

    Is that what you're looking for?
  7. Feb 15, 2009 #6
    Thank you all for your help so far.

    Well, I have used another approach in resolving this this problem but I am wondering if anyone could suggest a way to simplify this further. I wish to express this equation in terms of x:

    d = 10^-20 x^(-18/4) x^-1.

    So, is there a way to write this equation in the form: x = ....... ??

    I have checked my solution with numeric values which seems fine but I need to express in that form, please help. Thanks.
  8. Feb 15, 2009 #7
    To Mark44, HallsofIvy and other members who helped or looked into my posting, thanks so much!

    The good news is I finally resolved the problems and I am so glad I can now move on!
  9. Feb 16, 2009 #8


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    I just wish I knew clearly what those problems were!
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