A drug dispensed on a written prescription signed by a physician, dentist, or veterinarian (except a drug dispensed in the course of the conduct of a business of dispensing drugs pursuant to diagnosis by mail) shall, if (1) such physician, dentist, or veterinarian is licensed by law to administer such drug, and (2) such drug bears a label containing the name and place of business of the dispenser, the serial number and date of such prescription, and the name of such physician, dentist, or veterinarian, be exempt from the requirements of RCW 69.04.450 through 69.04.540.