Which book has the proof of $\sum_{n \leq x}\log^h(\frac x n)= O(x)$?

Question

I am looking for books that contains the proof of $\sum_{n \leq x}\log^h(\frac x n)= O(x)$.

EDITED QUESTION

I have the proof (in a lecture sheet), looking for a book for the reference.

According to one answer, the proof appears on p. 461 ff of the Sixth Edition of Hardy and Wright's An Introduction to the Theory of Numbers (Theorem 423).

But it looks like that is not the book I am looking for.

Is there any other book that contains the proof?

I have checked Tom M Apostol's Book.

Answer 1

The proof appears on p. 461 ff of the Sixth Edition of Hardy and Wright's An Introduction to the Theory of Numbers (Theorem 423).