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Math Help - Solve 4^x - 3.2^x + 2 = 0.

  1. #1
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    Solve 4^x - 3.2^x + 2 = 0.

    here it is:
    4^x - 3.2^x + 2 = 0

    i have a complete mindblank when i try and solve this....
    can anyone help me out?
    Last edited by mr fantastic; March 7th 2011 at 02:29 AM. Reason: Re-titled.
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  2. #2
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    \displaystyle 4^x - 3\cdot 2^x + 2 = 0

    \displaystyle \left(2^2\right)^x - 3\cdot 2^x + 2 = 0

    \displaystyle 2^{2x} - 3\cdot 2^x + 2 = 0

    \displaystyle \left(2^x\right)^2 - 3\cdot 2^x + 2 = 0.


    Let \displaystyle X = 2^x so that the equation becomes

    \displaystyle X^2 - 3X + 2 = 0.


    You should be able to solve for \displaystyle X and use this to solve for \displaystyle x.
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