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Math Help - converting parametric equasions to cartesian, slightly confused

  1. #1
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    converting parametric equasions to cartesian, slightly confused

    I've missed a few days of class due to illness and have fallen behind a bit. There is homework due and I have figured everything out but this.

    x(t)=e^7t
    y(t)=e^4t

    I have completely forgotten how to get a variable out of the exponent... >_<
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  2. #2
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    Re: converting parametric equasions to cartesian, slightly confused

    Quote Originally Posted by Kisolv View Post
    I've missed a few days of class due to illness and have fallen behind a bit. There is homework due and I have figured everything out but this.

    x(t)=e^7t
    y(t)=e^4t

    I have completely forgotten how to get a variable out of the exponent... >_<
    \begin{cases}y(t)=e^{4t} \\x(t)=e^{7t}\end{cases}

    hence :

    y=(e^t)^4=(e^{7t})^{\frac{4}{7}}=x^{\frac{4}{7}}
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  3. #3
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    Re: converting parametric equasions to cartesian, slightly confused

    Another way:

    \ln x = \ln {e^{7t}}=7t \Leftrightarrow t = \frac{\ln{x}}{7}

    y = e^{4t} = e^{\frac{4}{7}\ln{x}}=e^{\ln{x}^{4/7}}=x^{4/7}
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