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Question
\[\lim_{x \to \infty} \left( a^{1/x} - 1 \right)x\]
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Solution
\[\lim_{x \to \infty} \left( a^\frac{1}{x} - 1 \right)x\]
\[Let y = \frac{1}{x}\]
\[ x \to \infty \]
\[ \therefore y \to 0\]
\[ \Rightarrow \lim_{y \to 0} \left( \frac{a^y - 1}{y} \right)\]
\[ = \log a\]
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