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Proof that Limit of the Log is the Log of the Limit. What is the intuition behind this statement?

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1 Answer

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Logarithm is a continuous function, and in general, if $\lim\limits_{x \to c} g(x) = b$, and $f$ is continuous at $b$, then $f\left(\lim\limits_{x \to c} g(x)\right) = f(b) = \lim\limits_{x \to c} f\big(g(x)\big)$. – Henry Swanson

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