Is is true that $\lim(\ln x) = \ln(\lim x)$? [closed]

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As the title says, I want to ask everyone if $\lim(\ln x) = \ln(\lim x)$ when x approach to infinite with any function.

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2 Answers

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The function $\ln x:\mathbb{R^{+}}\to\mathbb{R}$ is a continuous function. So $\forall x_0 \in \mathbb{R^{+}} \ \ \lim_{x\to x_0 }\ln x =\ln x_0=\ln\lim_{x\to x_0}x$.

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$$\lim_{x\to\infty} \ln(x)=\infty$$ $$\ln\left(\lim_{x\to\infty}x\right)=\infty$$ If I understood what you were saying properly, it was a bit unclear..

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