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Math Help - Quadratic Equation

  1. #1
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    Question Quadratic Equation

    Express the quadratic equation y = x^2 as a linear equation using the substitution s = ln y, t = ln x.

    I have no idea how to start this.
    Any help is appreciated!
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  2. #2
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    Quote Originally Posted by live_laugh_luv27 View Post
    Express the quadratic equation y = x^2 as a linear equation using the substitution s = ln y, t = ln x.

    I have no idea how to start this.
    Any help is appreciated!
    Taking the natural log of both sides gives

    \ln y = \ln x^2 = 2 \ln x
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  3. #3
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    Quote Originally Posted by danny arrigo View Post
    Taking the natural log of both sides gives

    \ln y = \ln x^2 = 2 \ln x

    Ok...but where do the s and t come in??
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  4. #4
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    Quote Originally Posted by live_laugh_luv27 View Post
    Ok...but where do the s and t come in??
    If you let

     s = \ln y\; \text{and}\; r = \ln x gives s = 2r, a linear equation.
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  5. #5
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    Ok, thanks
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