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Simple equation, but I dont know how to solve for x

  1. Jun 4, 2006 #1
    without using a calculator's graphing or equation solver tools :tongue:

    2000x^16 + 5000x^39 = 3000 + 1600x^12
    how can i solve for x?

    200(1+i)^7 + 100(1+i)^5 = 300(1+i)^3
    i?

    1.06^t = 2(1.04)^t
    t?

    1.08^-n + 1.08^-2n = 1
    n?

    6x^2-2x-3=0
    argh why cant i do these.. i feel like im missing a basic technique that can be applied to all of these
     
    Last edited: Jun 4, 2006
  2. jcsd
  3. Jun 4, 2006 #2
    is it possible?
     
    Last edited: Jun 4, 2006
  4. Jun 4, 2006 #3
    bumpbumpbump
     
  5. Jun 4, 2006 #4

    arildno

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    As for the second, i=-1 is a solution.
    To find the other solutions, divide throughout with (1+i)^3, and introduce z=(1+i)^2.
     
  6. Jun 4, 2006 #5

    Tide

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    Are you sure you typed your first equation correctly?
     
  7. Jun 4, 2006 #6

    arildno

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    I was also wondering about that one.
    It is order of magnitudes more difficult to solve than the others.
     
    Last edited: Jun 4, 2006
  8. Jun 4, 2006 #7
    how about if the unkown is in the exponent
    like..
    1.06^t = 2(1.04)^t
    t?

    1.08^-n + 1.08^-2n = 1
    n?
     
  9. Jun 4, 2006 #8

    arildno

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    Use well-known logarithm rules for the first one, set [itex]x=1.08^{-n}[/itex] in the second one.
     
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