1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
    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

    User Avatar
    Homework Helper

    Plotting both sides would help to find all three roots.

    ehild
     
  5. Jan 5, 2012 #4

    jedishrfu

    Staff: Mentor

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook