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Math Help - Solving an exponential equation

  1. #1
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    Solving an exponential equation

    I'm a little stuck (again).

    How would I go about solving an equation like this:

    4^2^x-4^x-20=0

    And a more complicated one such as:

    2^x+12(2)^-^x=7

    All help greatly appreciated!
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by youngb11 View Post
    I'm a little stuck (again).

    How would I go about solving an equation like this:

    4^2^x-4^x-20=0
    This is a quadratic in 4^x and happily it will factor to (4^x-5)(4^x+4)=0. Note that 4^x > 0

    And a more complicated one such as:

    2^x+12(2)^-^x=7

    All help greatly appreciated!
    Multiply through by the LCD which is 2^x since 2^{-x} = \dfrac{1}{2^x}. You'll get 2^{2x} + 12 = 7 \cdot 2^x which, again, is a quadratic equation
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  3. #3
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     (4^{x})^{2} - 4^{x} - 20 = 0

    now let  u = 4^{x}
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  4. #4
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    Quote Originally Posted by e^(i*pi) View Post
    Multiply through by the LCD which is 2^x since 2^{-x} = \dfrac{1}{2^x}. You'll get 2^{2x} + 12 = 7 \cdot 2^x which, again, is a quadratic equation
    Thanks! However, I'm a little stuck once we get to 7 \cdot 2^x. The answer in the back of the book shows x=2 and x=\dfrac{log3}{log2}.

    How would we multiply 7 with 2^x but still come to such an answer?

    Thanks!
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  5. #5
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    Quote Originally Posted by youngb11 View Post
    Thanks! However, I'm a little stuck once we get to 7 \cdot 2^x. The answer in the back of the book shows x=2 and x=\dfrac{log3}{log2}.

    How would we multiply 7 with 2^x but still come to such an answer?

    Thanks!
    You were told what to do:
    Quote Originally Posted by e^(i*pi) View Post
    [snip]Multiply through by the LCD which is 2^x since 2^{-x} = \dfrac{1}{2^x}. You'll get 2^{2x} + 12 = 7 \cdot 2^x which, again, is a quadratic equation
    This is not the answer, it is how to get the answer. And how to do this was explained to you with the first question. Let 2^x = w. Re-arrange to get a quadratic equation in w that is equal to zero. Solve for w. Hence solve for x.

    Please make an atttempt. Show your work, say where you get stuck if you need more help.
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  6. #6
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    Quote Originally Posted by mr fantastic View Post
    This is not the answer, it is how to get the answer. And how to do this was explained to you with the first question. Let 2^x = w. Re-arrange to get a quadratic equation in w that is equal to zero. Solve for w. Hence solve for x.

    Please make an atttempt. Show your work, say where you get stuck if you need more help.
    Ah, okay. It's much clearer when you replace 2^x for W. Thanks again!
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