Question

$\underset{x\to \infty }{\lim }\left(a^{1/x}-1\right)x$

Answer 1

$$\begin{gathered} \underset{x\to \infty }{\lim }\left(a^{\frac{1}{x}}-1\right)x \\ \mathrm{Let}y=\frac{1}{x} \\ x\to \infty \\ \therefore y\to 0 \\ \Rightarrow \underset{y\to 0}{\lim }\left(\frac{a^y-1}{y}\right) \\ =\log a \end{gathered}$$