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Math Help - Solve for y as a function of x

  1. #1
    Junior Member xterminal01's Avatar
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    Solve for y as a function of x

    The Eq is supposed to be solved for Y as a function of X :


    y^x = x^y + 1
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  2. #2
    GAMMA Mathematics
    colby2152's Avatar
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    Quote Originally Posted by xterminal01 View Post
    The Eq is supposed to be solved for Y as a function of X :


    y^x = x^y + 1
    Take the natural log of both sides...

    xln|y|=yln|x|
    \frac{y}{x}=\frac{ln|y|}{ln|x|}
    \frac{y}{x}=log_xy

    I'm now as lost as you are...
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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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    Recall \log(a+b) has not property.
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  4. #4
    Junior Member xterminal01's Avatar
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    Set  g(x,y)=y^{x}-x^{y}-1

     \frac{\partial{g}}{\partial{y}}=xy^{x-1}-x^{y}\ln(x),
    whose value at (1,2) equals 1 ? Is this correct?
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