title: Solve recurrence relation by master theorem
body: <p>I am confused here which case of master theorem finding tight bound for this recurrence  relation: </p>
  
  <p><strong>T(n) = 27T(n/3) + Q(n<sup>3</sup>log n)</strong></p>
  
  <p>Here is my solution:<br>
     f(n) = n<sup>3</sup>log n<br>
     a=27 b = 3 so </p>
  
  <p><img src="https://i.stack.imgur.com/HnDpx.png" alt=""></p>
  
  <p>So we can see here that <strong>f(n) > n<sup>3</sup></strong><br>
   So this: <img src="https://i.stack.imgur.com/k0bFw.png" alt=""></p>
  
  <p>Case 3 will apply: correct me if I am wrong here.<br>
  Note:  But it's answer is coming n<sup>3</sup>log<sup>2</sup>n which is coming by case 2 of Master Theorem. Which one should I apply?</p>