Difference between $\log n$ and $\log^2 n$
Solution 1:
$(\log(n))^2$ means $\log^2(n)$
Solution 2:
Yes, There is a huge difference.
If$$x=\log n$$ Then$$x^2=\log^2n$$
Solution 3:
$$\lim_{n\to\infty}\frac{\log^2 n}{\log n} = \infty,$$
intuitively meaning that as $n\to\infty$, an $O(\log^2 n)$ time complexity algorithm takes infinitely times as much time as an $O(\log n)$ time complexity algorithm.