multiple of an integer and asymptotics Let us suppose that we have a positive integer $N$.
We take the integer $\lceil \log_2 N \rceil$. Does there always exist an integer $X \geq N$ such that the following both conditions are satisfied:
1) $X$ is a multiple of $\lceil \log_2 N \rceil$
2) $X=O(N)$
?

Hint. One may take
$$
X= \lceil N/\log_2 N \rceil \lceil \log_2 N \rceil.
$$
