Involving Landau's 'big oh' notation

[Reb]

(don't have an answer yet)

We say that two sequences f,g are f=O(g) if-f there is a c>0 such that |f(n)|<c|g(n)| uniformly as n tends to infinity.

If g(n)>2, does f=O(g) imply lnf=O(ln(g))?

 

[mathman]

|f(n)| < c|g(n)| => ln(|f(n)|) < ln(c) + ln(|g(n)|). You should have |f(n)|, c > 1 to avoid problems with abs. value of logs.