This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2009 Romania National Olympiad, 1
[b]a)[/b] Show that two real numbers $ x,y>1 $ chosen so that $ x^y=y^x, $ are equal or there exists a positive real number $ m\neq 1 $ such that $ x=m^{\frac{1}{m-1}} $ and $ y=m^{\frac{m}{m-1}} . $ [b]b)[/b] Solve in $ \left( 1,\infty \right)^2 $ the equation: $ x^y+x^{x^{y-1}}=y^x+y^{y^{x-1}} . $
function equation unique solution algebra

2011 Bogdan Stan, 3
Solve in $ \mathbb{R} $ the equation $ 4^{x^2-x}=\log_2 x+\sqrt{x-1} +14. $ [i]Marin Tolosi[/i]
function unique solution algebra