Question

$\underset{x\to 0}{\lim }\frac{a^x+b^x+c^x-3}{x}$

Answer 1

$$\begin{gathered} \underset{x\to 0}{\lim }\left[\frac{a^n+b^n+c^n-3}{x}\right] \\ =\underset{x\to 0}{\lim }\left[\frac{\left(a^n-1\right)}{x}+\frac{\left(b^n-1\right)}{x}+\frac{\left(c^n-1\right)}{x}\right] \\ =\log a+\log b+\log c \\ =\log \left(abc\right) \end{gathered}$$