It should be logn because in worst case the recurrence relation will be
T(n) = T(9*n/10) + 1
and we use master theorem to solve this relation then
T(n) = T(9*n/10) + 1
where a = 1, b = 10/9,
So nlogba = n log10/91
= n0
= 1
and f(n) = 1
so this holds the second case where,
if f(n) = nlogba logkn then T(n) = nlogbalogn
so in this case k = 0 , hence our solution is T(n) = logn