mysql> explain SELECT * FROM user_test WHERE first_name = 'cee' AND user_id = 199559;
+----+-------------+-----------+-------+--------------------------+---------+---------+-------+------+-------+
| id | select_type | table     | type  | possible_keys            | key     | key_len | ref   | rows | Extra |
+----+-------------+-----------+-------+--------------------------+---------+---------+-------+------+-------+
|  1 | SIMPLE      | user_test | const | PRIMARY,first_name_index | PRIMARY | 4       | const |    1 | NULL  |
+----+-------------+-----------+-------+--------------------------+---------+---------+-------+------+-------+
1 row in set (0.00 sec)

mysql> explain SELECT * FROM user_test WHERE first_name = 'cee' AND date_of_birth = '2019-10-13';
+----+-------------+-----------+-------------+---------------------+-----------------------+---------+------+------+---------------------------------------------------------+
| id | select_type | table     | type        | possible_keys       | key                   | key_len | ref  | rows | Extra                                                   |
+----+-------------+-----------+-------------+---------------------+-----------------------+---------+------+------+---------------------------------------------------------+
|  1 | SIMPLE      | user_test | index_merge | first_name_index,   | date_of_birth_index,  | 4,152   | NULL |    1 | Using intersect(date_of_birth_index,first_name_index);  |
|    |             |           |             | date_of_birth_index | first_name_index      |         |      |      | Using where                                             |
+----+-------------+-----------+-------------+---------------------+-----------------------+---------+------+------+---------------------------------------------------------+
1 row in set (0.00 sec)