What is the big o notation of following functions

Question

I can't figure out the smallest upper barriers for those two functions.

I think ex1 has O(log_3(n)) and ex5 should have O(n!). But I'm not actually confident about this, since I haven't truly understood the subject yet.

public int ex1 ( int n ) {
    int r = 0 ;
    for ( int i = 1 ; i < n ; i++) {
        r += n ;
        n = n / 3 ;
    }
    return r ;
}

public static int ex5 ( int n ) {
    int r = 1 ;
    for ( int i = 0 ; i < n ; i ++) {
            r += ex5 ( n - 1 ) ;
    }
    return r ;
}

Answer 1

The output values of ex5 correspond to sequence A000522 at oeis.org, which increases as a(n) = Sum_{k=0..n} n!/k! (or n! to a first approximation). Because of the horrible way this function is coded, this is equal to the function's time complexity.

A much better algorithm would be as follows:

public static int ex5 ( int n ) {
    return (n) ? 1 + n * ex5(n-1) : 1;
}

which is obviously O(n^2) O(n) ^{(Sorry, it's late and I need sleep!)}.

EDIT: As everyone else is saying, the complexity of ex1 is O(log_3(n)), or simply O(log(n)), since log_3(n) = log(n)/log(3), and log(3) is a constant in any base.