Proof that Limit of the Log is the Log of the Limit

calculus limits

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


Solution 1:

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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