The recurrence relation for binary search is
T(n) = T(n/2) + 2, T(1) = 1
The recurrence relation for ternary search is
T(n) = T(n/3) + 4, T(1) = 1
Time Complexity for Binary search = 2clog2n + O(1)
Time Complexity for Ternary search = 4clog3n + O(1)
Therefore, the comparison of Ternary and Binary Searches boils down the comparison of expressions 2Log3n and Log2n . The value of 2Log3n can be written as (2 / Log23) * Log2n . Since the value of (2 / Log23) is more than one, Ternary Search does more comparisons than Binary Search in worst case.