title: insertion sort beat merge sort n<=8logn , value of n
body: <p>I am weak in math</p>
  
  <p>n&lt;=8logn  How to solve this equation to get the value of n,</p>
  
  <p>The question was from algorith "  For inputs of size n, insertion sort runs in 8n^2 steps while merge sort runs in 64n lg n steps; for which values of n does insertion sort beat merge sort?</p>
  
  <p>so i figured until.. </p>
  
  <pre><code>8n^2&lt;=64nlogn
  </code></pre>
  
  <p>n^2&lt;=8nlogn
  n&lt;=8logn</p>
  
  <p>but how to get value of n from here , full math would be helpful and any link to learn basic logarith math is appreciated. Thanks</p>