A calculus problem by crazy singh

Calculus Level 2

if

\( \lim _{ x\to \infty } \frac { \ln { { x }^{ n } } - \left[ x \right] }{ \left[ x \right] } = a\)

where \( \left[ x \right] \) denotes the integral part of \( x \)

Then \( { a }^{ 2 }\) is equal to ?

note: \(n\) is any real number.

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