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, .

Also, .

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):

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