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Solving equation with power of x in it

  1. Jan 5, 2012 #1
    1. The problem statement, all variables and given/known data
    [tex]x^2+1=2^x[/tex]

    2. Relevant equations
    N/A

    3. The attempt at a solution
    [tex]x^2 + 1 = 2^x[/tex]
    [tex]\log_2(x^2+1) = log_22^x[/tex]
    [tex]log_2(x^2+1)=x[/tex]
    Get stuck at this point - don't know where to go next. Please help!

    With very many thanks,

    Froskoy.
     
  2. jcsd
  3. Jan 5, 2012 #2

    micromass

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    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    This equation cannot be solved analytically. There is no technique to find the correct answer. Either you

    1) Guess a solution and prove that it is the correct one.
    2) Use the Lambert W function to find an expression for the solution.
    3) Find a solution numerically.

    (1) will work here. But it remains to prove here that the guessed solutions are the only solutions.
     
  4. Jan 5, 2012 #3

    ehild

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    Homework Helper
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    Plotting both sides would help to find all three roots.

    ehild
     
  5. Jan 5, 2012 #4

    jedishrfu

    Staff: Mentor

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