title: Big O Log problem solving
body: <p>I have question that comes from a algorithms book I'm reading and I am stumped on how to solve it (it's been a long time since I've done log or exponent math). The problem is as follows:</p>
  
  <p>Suppose we are comparing implementations of insertion sort and merge sort on the same
  machine. For inputs of size n, insertion sort runs in 8n^2 steps, while merge sort runs in 64n log n steps. For which values of n does insertion sort beat merge sort?</p>
  
  <p>Log is base 2. I've started out trying to solve for equality, but get stuck around n = 8 log n.</p>
  
  <p>I would like the answer to discuss how to solve this mathematically (brute force with excel not admissible sorry ;) ). Any links to the description of log math would be very helpful in my understanding your answer as well.</p>
  
  <p>Thank you in advance!</p>