Can someone please show me, if possible, how to evaluate the following limit without using L'Hospital's rule?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\mathop {\lim }\limits_{x \to \infty } \left( {1 - \frac{2}{{\log _e n}}} \right)^{\log _e n}

[/tex]

The answer is e^(-2).

Rewriting the terms in the bracket as a single term doesn't appear to get me anywhere. I tried taking the logarithm and exponentiating the limit but that still ended up requiring me to use L'Hospital's rule. Any help with evaluating the limit without using L'Hospital's rule would be good thanks.

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# Evaluate the following limit without using L'Hospital's rule?

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