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Math Help - Help solving an exponential equation algebraically!

  1. #1
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    Help solving an exponential equation algebraically!

    I need to solve this algebraically. I already know the answer, which is +/-2.2604 or (log(5/2 +/- (rt21)/2))/(log(2)). I just need to know HOW to get there.
    The equation:
    2^x + 2^(-x) = 5
    I tried solving it using factoring/quadratics, but couldn't figure out how to set it up.
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  2. #2
    Senior Member eumyang's Avatar
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    2^x + 2^{-x} = 5

    Multiply both sides by 2^x:
    2^{2x} + 1 = 5\cdot 2^x

    Put all terms on one side:
    2^{2x} - 5\cdot 2^x + 1 = 0

    If you let w = 2^x, then this looks like a quadratic:
    w^2 - 5w + 1 = 0

    Solve for w (using the quadratic formula is probably the easiest), but don't forget to replace w with 2^x afterwards and solve for x.
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  3. #3
    Pim
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    2^x+2^(-1)=5
    2^x + \frac{1}{2^x}=5
    (2^x)^2 + 1 = 5*2^x
    p = 2^x
    p^2 + 1 = 5p
    p^2-5p+1 = 0

    Can you take it from here?
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  4. #4
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    Yup, I figured it out!! Thanks so much. I kept trying to keep the 2^(-x) as the bx term, but it never crossed my mind to multiply and make 5 the second term. Thanks again.
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