I am revising for my exams and this question appears on a past paper:
Show that O(loga n) = O(logb n) for any choice of logarithmic bases a and b working from the mathematical definition of the order notation f(n) E O(g(n)).
Could someone please show me how to solve this?
The rule for changing base of a logarithm is: log_b(n) = log_a(n) / log_a(b).
This immediately implies log_b(n) = O(log_a(n)) and by symmetry log_a(n) = O(log_b(n)).