title: Proof of O(loga n) = O(logb n), for any base a or b
body: <p>I am revising for my exams and this question appears on a past paper:</p>
  
  <p>Show that <strong>O(loga n) = O(logb n)</strong> for any choice of logarithmic bases a and b working from the mathematical definition of the order notation f(n) E O(g(n)).</p>
  
  <p>Could someone please show me how to solve this?</p>