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Find the minimum of $x-y$ among all ordered pairs of real numbers $(x, y)$, $x$ and $y$ between 0 and 1, where there exists a real number $a \\eq 1$ such that \[ \log_{x}a + \log_{y}a = 4\log_{xy}a. \]

User Kemakino
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The solution is on the added picture
Find the minimum of $x-y$ among all ordered pairs of real numbers $(x, y)$, $x$ and-example-1
User Karim Pazoki
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