How to solve the following sequence limit:

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Find $\lim_{n \rightarrow \infty} a_n$ where $$ a_n=\Bigg(\frac{3n^2}{3n^2-1}\Bigg)^{2n^2+3}$$

How to even start with an exponent problem like this ?

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Hint : Take logarithm both side and then take $n \to \infty$