You can solve it using substitution method.
Here base condition T(1)=0 must be given
T(n) = T(n-1) + logn
T(n-1) = T(n-2) + log(n-1)
T(n-2) = T(n-3) + log(n-2)
.
By substituting..
T(n) = T(n-3) + logn + log(n-1) + log(n-2)
T(n) = T(n-(n-1)) + logn + log (n-1) + log(n-2) + ........ + log(n-(n-2))
T(n) = T(1) + log (n * (n-1) * (n-2) * (n-3) ..... (n-(n-2)) [multiplication goes upto (n-1) times]
T(n) = T(1) + log(n(n-1))
T(n) = 0 + (n-1) log n
T(n) = O(nlogn)