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If $\lim _{x \rightarrow 2} \frac{x^n-2^n}{x-2}=80$, where $n$ is a positive integer, then $n=$
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$5$
$\lim _{x \rightarrow 2} \frac{x^n-2^n}{x-2}=n \cdot 2^{n-1} \Rightarrow n \cdot 2^{n-1}=80 \Rightarrow n=5$ (using L-Hospital's rule)
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