I have been looking at the question as to which grows faster asymptotically; $\log \sqrt n$ or $4 \log n$. I have applied L'Hopitals rule and ended up with 1/8. This would imply that they grow at same rate.
Graphically $4 \log n$ is always above $\log \sqrt n$. Also from a perspective that $4 \log n$ is $\log n^4$ would imply intuitively that growth of $4 \log n$ is faster asymptotically
There appear to be contradictions.