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Calculus Level 5

If\[\lim _{ x\rightarrow 0 }{ \frac { \cot ^{ -1 }{ \left( { x }^{ -a }\log _{ a }{ x } \right) } }{ \sec ^{ -1 }{ \left( { a }^{ x }\log _{ x }{ a } \right) } } } =m\]

and\(a>1\).Find the value of \(5m\)

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