# Solve for y as a function of x

• December 7th 2007, 10:26 AM
xterminal01
Solve for y as a function of x
The Eq is supposed to be solved for Y as a function of X :

$y^x = x^y + 1$
• December 7th 2007, 11:24 AM
colby2152
Quote:

Originally Posted by xterminal01
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...
• December 7th 2007, 11:29 AM
Krizalid
Recall $\log(a+b)$ has not property.
• December 7th 2007, 01:12 PM
xterminal01
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?