Can I say $\log{O(n)}$?

Question

Suppose $e^{f(x)} = O(x)$, or equivalently, there exists a $c$ such that for all $x$, $f(x) \lt \ \log{x} + c$. Is $f(x) = \log{O(x)}$ generally understood to mean the same thing?

Answer 1

The standard is to write O(log n).

See also: https://stackoverflow.com/questions/2307283/what-does-olog-n-mean-exactly