Logs!!..But no wood..- part 2

Algebra Level 3

If \(\log _{ ab }{ a=4 }\), then the value of

\(\log _{ ab }{ \left( \frac { \sqrt [ 3 ]{ a } }{ \sqrt { b } } \right) } =\frac { x }{ y }\) where x and y are coprime integers. Find the value of \({ \left( x-y \right) }^{ 2 }\)

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