Problem For Year 2029

Algebra Level 5

If x>y>1x>y>1 and 1logxy+1logyx=2029\dfrac{1}{\log_xy}+\dfrac{1}{\log_yx}=\sqrt{2029}, find the value of 1logxyx1logxyy\dfrac{1}{\log_{xy}x}-\dfrac{1}{\log_{xy}y}.

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