Hoi, is there a way we can conclude that

$\displaystyle \lim_{n\to\infty}\frac{a_1+\cdots + a_n }{n} = \infty$ from the assumption that for some positive constant $\displaystyle K$

$\displaystyle \lim_{n\to\infty}\frac{\log(a_1)+\cdots \log(a_n)}{n} = K$

I need it for something, but i'm not even sure if it's true...?

The $\displaystyle a_n\geq 1$ are positive integers.