Which grows asymptotically faster, $\log \sqrt{n}$ or $4 \log n$?
The asymptotic growth of
$4 \log n$ is referred to as $\Theta(\log n)$.  You will have to look at
the definition of asymptotic growth to see why that is the case, but
intuitively, it is the growth of a function when we discard constant
factors and only look at the function &quot;in the limit&quot;.
You have found out that the difference between the two functions &quot;is
1/8&quot;, which makes sense, and which would put these two functions in the
same &quot;growth class&quot;.
When it comes to $\Theta\left(\log ( \sqrt n ) \right)$, it is, as you
likely have found out
$$\Theta\left(\log ( n^{1/2} ) \right) = \Theta\left( \frac{1}{2}\log n
\right) = \Theta\left(\log n \right).$$