The value of $\mathop {\lim }\limits_{x \to a} \frac{{\log \left( {x - a} \right)}}{{\log \left( {{e^x} - {e^a}} \right)}}$, is

JEE MATHEMATICS MCQ: LIMITS

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The value of

\lim\limits_{x \to a} \frac{{\log \left( {x - a} \right)}}{{\log \left( {{e^x} - {e^a}} \right)}}

, is

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Correct option: A

Option A (1) is correct because applying L'Hopital's rule or using the definition of the derivative, the limit evaluates to 1.

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