${lim}_{h \to \infty} (a^{\frac{1}{x}} - 1) x$

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Solution

${lim}_{h \to \infty} (a^{\frac{1}{x}} - 1) x$

Let $\frac{1}{x} = h$ as $x \to \infty, h \to 0$

$= {lim}_{h \to 0} \frac{(a^{h} - 1)}{h}$

$= l o g a$

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