agree 5 weighing for N=128 (worst case scenario you reduce to 43 15 5 2 1 after each consecutive weighing)

the last test case provided by the author is wrong: should be 5 since log(128)/log(3) < 5.

The problem is that the author do not specify an strategy. And as mentioned, dividing by 3 yields a better strategy than 6 weightings for 128. But, my guess is that the author counted the number of divisions instead of the number of weightings 128->[42 42 43] -> [14 14 14; 14 14 15]->[5 5 4; 5 5 5]->[2 2 0; 2 2 1]->[1;2]->1.