Show that implies .
implies there exists constants such that for all :
Let us assume so that . With that assumption we can write:
And if we take logarithm of all the terms, we can write:
If is large enough, .
The third line comes from the fact that and we can choose in such a way that .
From (1) and (2):
From (1) and (3):
Combining (4) and (5):