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Is this imposible?

  1. Sep 24, 2010 #1
    Find the solutions of 5^x=2x+1 by ordinary methods? if it can´t be found by these ways, then prove that it's imposible.
  2. jcsd
  3. Sep 24, 2010 #2
    It depends on what you mean by ordinary methods.

    By inspection, x=0.
  4. Sep 24, 2010 #3
    but, there is other answer, how you find it?
  5. Sep 25, 2010 #4


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    Gold Member

    The exponent ^5 is behind the X or after?
  6. Sep 25, 2010 #5
    Ordinary method consists in studying the function y=(5^x)-(2x+1)
    This shows that two roots exist (one of them is obvious).
    Drawing the graph of the function allows to obtain a first approximate of the second root.
    Then, numerical computation leads to the value of the root, as accurate as we want. There are a lot of numerical methods : Newton-Raphson and many other...
    Analytical solving is outside the scope of ordinary methods. It requires the use of a special function : the Lambert W function.

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