Searching for an element in a balanced binary search tree with n elements has a time complexity of O(log n).

Explanation:
In a balanced binary search tree, each node has at most two children, and the left child is always smaller than the parent node while the right child is always greater. This property allows for efficient searching.

When searching for an element in a binary search tree, we start from the root node and compare the target value with the value of the current node. If the target value is smaller, we move to the left child; if it is greater, we move to the right child. We continue this process until we find the target value or reach a leaf node, which indicates that the element is not present in the tree.

The time complexity of searching in a binary search tree depends on the height of the tree. In a balanced binary search tree, the height is logarithmic with respect to the number of nodes. This is because at each level, the number of nodes doubles, and the maximum height is reached when the tree is perfectly balanced, resulting in a logarithmic height.

Key Points:
- Balanced binary search trees have a logarithmic height.
- The height of a balanced binary search tree is logarithmic with respect to the number of nodes.
- Searching in a binary search tree involves comparing the target value with the current node and moving left or right accordingly.
- The time complexity of searching in a balanced binary search tree is O(log n).