Master theorem recurrence relation
Plotting isn't foolproof: for any $k,\varepsilon&gt;0$, we have $\log^kn = o(n^\varepsilon)$ (here, I've cancelled the common term of&nbsp;$n^2$). However, you can need to take $n$ really big to see it when $\varepsilon$&nbsp;is small (e.g., $0.095$) and $k$&nbsp;isn't so small (e.g., $5$).  Here's the plot for $0\leq n\leq 10^{131}$, again with the $n^2$&nbsp;term cancelled, and it looks quite different from your plot up to $n=10^5\,$!

Indeed, this question may even have been designed to catch you out if you try to compare the asymptotic growth by plotting instead of by understanding.