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Math Help - Nonlinear Equation

  1. #1
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    Nonlinear Equation

    Is there an easy way to solve nonlinear equations such as

    2^(x^3-4x) = (x - 1)

    besides graphing?

    Also how would you go about solving 16^(x+2) = 8^x
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  2. #2
    Senior Member JaneBennet's Avatar
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    I’m not sure about the first equation, but the second equation can be solved by taking logarithm to base 2.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by BarlowBarlow1 View Post
    Is there an easy way to solve nonlinear equations such as

    2^(x^3-4x) = (x - 1)
    There are numerical techniques, if you don't consider that to be graphing. I believe that you can also express the solution in terms of the Lambert W function, but this is technically an approximation as well.

    -Dan
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  4. #4
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    Hello, BarlowBarlow1!

    Is there an easy way to solve nonlinear equations such as

    2^{x^3-4x} \:= \: x - 1 .besides graphing?
    Well, the answer can be approximated by any of several available methods.


    Solve: . 16^{x+2} \:= \:8^x

    We have: . (2^4)^{x+2} \:=\:(2^3)^x\quad\Rightarrow\quad2^{4x+8} \:=\:2^{3x}

    Therefore: . 4x + 8 \:=\:3x\quad\Rightarrow\quad x \:=\:-8

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