Question

$\underset{x\to 0}{\lim }\frac{5^x+3^x+2^x-3}{x}$

Answer 1

$$\begin{gathered} \underset{x\to 0}{\lim }\left[\frac{5^x+3^x+2^x-3}{x}\right] \\ =\underset{x\to 0}{\lim }\left[\frac{5^x-1}{x}+\frac{3^x-1}{x}+\frac{2^x-1}{x}\right] \\ =\log \left(5\right)+\log \left(3\right)+\log \left(2\right) \\ =\log \left(5\times 3\times 2\right) \\ =\log 30 \end{gathered}$$