System of 2 equations:

[tex]\begin{tabular}{|l}x^{y} = y^{x}\\x^{3} = y^{2} \end{tabular}[/tex]

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System of 2 equations:

[tex]\begin{tabular}{|l}x^{y} = y^{x}\\x^{3} = y^{2} \end{tabular}[/tex]

[tex]\begin{tabular}{|l}x^{y} = y^{x}\\x^{3} = y^{2} \end{tabular}[/tex]

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**Posts:**405**Joined:**Sun Oct 09, 2005 11:37 am**Reputation:****26**

[tex]log_{x} x^{y}=log_{x} y^{x}[/tex](x>0 from the second equation) [tex]\Leftrightarrow y=x.log_{x}y[/tex] (1)

Similarly from the second equation [tex]log_{x}x^{3}=log_{x}y^{2} \Leftrightarrow log_{x}y=\frac{3}{2}[/tex] (2).

From (1) and (2) [tex]y=\frac{3x}{ 2}[/tex]. Then again from the second equation of the system we have [tex]x^{3}=\frac{9}{4 }x^{2}[/tex] and it is easy then...

Similarly from the second equation [tex]log_{x}x^{3}=log_{x}y^{2} \Leftrightarrow log_{x}y=\frac{3}{2}[/tex] (2).

From (1) and (2) [tex]y=\frac{3x}{ 2}[/tex]. Then again from the second equation of the system we have [tex]x^{3}=\frac{9}{4 }x^{2}[/tex] and it is easy then...

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