title: Asymptotically comparing n⁽¹⁰ ˡᵒᵍ ⁿ⁾ and (log n)ⁿ
body: <p>I've got this problem as home-task in computer science (data structures): find and compare the big-O complexity of the following functions: </p>
  
  <ul>
  <li>f(n) = n<sup>10 log n</sup></li>
  <li>g(n) = (log n)<sup>n</sup></li>
  </ul>
  
  <p>I've tried a number of things like noting that n<sup>10log n</sup> = O(n<sup>n</sup>) and that (log n)<sup>n</sup> = O(n<sup>2</sup>) as well, but that's not helping me here. Any advice about how to solve this?</p>