Additional evidence for the halogenation mechanisms that we just presented comes from the following facts: (a) Optically active 2 -methyl-1-phenylbutan-1-one undergoes acid-catalyzed racemization at a rate exactly equivalent to the rate at which it undergoes acid-catalyzed halogenation. (b) 2 -Methyl-1-phenylbutan-1-one undergoes acid-catalyzed iodination at the same rate that it undergoes acid-catalyzed bromination. (c) 2 -Methyl1-phenylbutan- 1-one undergoes base-catalyzed hydrogen-deuterium exchange at the same rate that it undergoes base-promoted halogenation. Explain how each of these observations supports the mechanisms that we have presented.