Limit of Logarithm Function (Jee Mains)

Evaluation of Limits

Medium

Limit of Logarithm Function

Let f : R → (0, ∞) be a twice differentiable function such that f(3) = 18, f'(3) = 0 and f "(3) = 4.
Then $\mathop {\lim }\limits_{x \to 1} \left( {{{\log }_e}{{\left( {\frac{{f(2 + x)}}{{f(3)}}} \right)}^{\frac{{18}}{{{{(x - 1)}^2}}}}}} \right)$ is equal to :

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