I am attempting to write a program that determines whether a specific license plate is one of 10,000 that I have stored. I want to write a fast response algorithm first and foremost, with memory usage as a secondary objective. Would a balanced binary search tree or a hash table be more sufficient in storing the 10,000 license plate numbers (which also contain letters)?
A hash table takes O(1) time to look up any given entry (i.e. to check whether or not it is in the data structure), whereas a binary search tree  takes O(logn) time. Therefore, a hash table will be a more efficient option in terms of response speed. 
Binary search trees are more useful in scenarios where you need to display things in order, or find multiple similar entries.
Best Data Structure for storing license plates and searching if a given license plate exists