Is an O(log n) linked list search algorithm possible?
An O(log n) algorithm would require to

divide the list into a fixed number of parts in constant time, and
determine in which of the parts the searched item is in constant time.

e.g. for a binary search algorithm for a sorted indexed array data structure which keeps track of its size, the split point can be calculated directly from the size of the array, and it can be determined whether the searched item is in the first or second half by a comparison with the item at the split point.
But for a linked list, you don't know its size and would have to traverse it in order to find the split points. This is an O(n) operation, so the overall algorithm can't be O(log n).
In general, the second requirement is also not satisfied.
Is it possible for a search algorithm for linked lists to be O(log n)? From my understanding, linked lists could have either O(n) or O(1) since you can choose where to start, from the start of the link list to the end. Knowing this, can you start in the middle for a searching algorithm that runs in O(log n) time?