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Simple log question

  1. May 16, 2005 #1
    Help me solve for x in detail please:

    8^x+13^x=108

    Simply done graphically, but algebraically?
     
  2. jcsd
  3. May 16, 2005 #2

    Zurtex

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    It can't be solved with logs or anything like that.
     
  4. May 16, 2005 #3
    I figured as much after working with it for a while, but I thought I might have just been missing something. How does one solve it then?
     
  5. May 16, 2005 #4

    Zurtex

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    You can only approximate the solution, which is:

    [tex]x \approx 1.682790571570192534987737142973064792462[/tex]
     
  6. May 16, 2005 #5

    dextercioby

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    I think you can't do it,without a calculator.Maple returns [itex] \left\{ x=1.\,68279\,0572\right\} [/itex],but it can't be solved algebraically.In fact,most transcendental equations can't be solved.

    Daniel.
     
  7. Jun 16, 2005 #6
    you can solve it by using newton-raphson method
     
  8. Jun 16, 2005 #7

    Curious3141

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    Only approximate, not an exact solution. There is no exact solution method.
     
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