what is the time complexity of this code ? (log3n)

Question

I have this code and I have to know the time complexity of it, I am a beginner in this subject and it confuses me a little bit.

void func(int n){
   while(n > 0 && n % 3 ==0){
       do_computation(n);
       n = n/3;
   }
}

the function do_computatation have a time complexity of 1 then the worst case of func would be O(log3n) is that right ?

Answer 1

Yes, it's O(log₃n), but that's the same as O(log n). The base doesn't matter, since log_an = (log_ab)(log_bn), and constant factors don't matter.

EDIT:

log(a^b) = b log(a) (in any base)

n = b^log_bn
Take log_a of both sides:
log_an = log_a(b^log_bn)
=(log_bn)(log_ab)