Here Answer should be O(nlogn)
lets see how!
T(n) = T(n-1) +logn ----1
T(n-1) = T(n-2) + log(n-1) -----2
T(n) = T(n-2) +logn +log(n-1) using 2nd.
T(n-2) = T(n-3) + log(n-2) ---3
T(n) = T(n-3) +logn +log(n-1)+log(n-2)
so by following this pattern we can write
T(n) = T(n- (n-1)) + log 1 + log 2+ log3+ ............+ log(n-1) +logn
as we know logn +log(n-1) = log(n)(n-1)
therefor T(n) = T(1) + logn.(n-1).(n-2)......3.2.1
T(n) = T(1) + logn!
and log n!<= nlogn
therefor this is O(nlogn)