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Math Help - need help with solving equations

  1. #1
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    need help with solving equations

    This form of equation cause me a lot of problems. I know it involves several steps, but i am getting stuck right at the start.

    2^x + 2^-x =5

    My teacher said to start it off by setting it equal to zero, but after that I don't know what to do.
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  2. #2
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    Quote Originally Posted by mtt0216 View Post
    This form of equation cause me a lot of problems. I know it involves several steps, but i am getting stuck right at the start.

    2^x + 2^-x =5

    My teacher said to start it off by setting it equal to zero, but after that I don't know what to do.
    multiply each term by 2^x ...

    2^{2x} + 1 = 5 \cdot 2^x

    let u = 2^x ...

    u^2 + 1 = 5u<br />

    u^2 - 5u + 1 = 0

    u = \frac{5 \pm \sqrt{21}}{2}

    2^x = \frac{5 + \sqrt{21}}{2}

    2^x = \frac{5 - \sqrt{21}}{2}


    finally, use logarithms to solve for x
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  3. #3
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    thanks a lot .. How would this problem change if e was substituted for 2.
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  4. #4
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    Quote Originally Posted by mtt0216 View Post
    thanks a lot .. How would this problem change if e was substituted for 2.
    no change ... in fact, would make the final step easier when solving using the natural log.
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