Big O Asymptotic complexity
The answer is correct. Let's verify it

$\log_{10}n $ and $\log{n}$ belong to the complexity class $O(\log{n})$, because they differ by a constant factor, hence $\log_{10}n \asymp \log{n}$. 

$n^{0.8} \succ \sqrt{n}$, because $0.8 &gt; \frac{1}{2}$. The last pair $n\log{n}$ and $n\log{n}^2$ belong to the complexity class $O(n\log{n})$ because they also differ by a constant factor ($n\log{n^2} = 2n\log{n}$), hence  $n\log{n} \asymp n\log{n^2}$. Finally we'll show that $\sqrt{n} \succ \log{n}$ and $n\log{n} \succ n^{0.8}$. The last one is obvious and I'll leave to you to prove that $\sqrt{n} \succ \log{n}$ (I claim that is true, if you face problems with it I'll expand the answer with proof).