Given a sorted array nums and a value target, find the index of target in the array using recursion — or return -1 if it isn't present. Sortedness turns "which half could possibly contain the target?" into a question answerable in O(1): compare the target against the middle element, and an entire half of the array can be ruled out immediately, no matter how large the array is. Express that as a recursive call on whichever half survives, narrowing the window (given by a low and high bound) with every call, until either the target is found or the window collapses to nothing (the base case). Each call does a constant amount of work and halves the remaining search space, so the total number of calls needed is O(log n) — a linear scan's worst case shrinks to a logarithmic one, purely by using the fact that the array is sorted.