Question

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 \(a \neq 1\) such that
\( \log_{x}a + \log_{y}a = 4\log_{xy}a. \)

Answer 1

really not my bag but i notice that if you base shift the logs you lose the a and conclude that x = y