I am currently studying for my final in algorithms. This is not a homework problem and comes from an old final exam.
Show that f(n) = 4logn + log log n is big theta of logn.
It is obvious that log log n is considerably smaller than log n and thus insignificant. But how can I show it formally? I'm familiar with limits and L'hopital so I would appreciate it if you can show me how to do it with that method.