Final answer:
The nerve that transmits pain in the patient's tongue is CN V3 (lingual).
Step-by-step explanation:
The nerve that transmits pain in the patient's tongue is the CN V3 (lingual). The facial and glossopharyngeal nerves convey gustatory stimulation to the brain. Along with taste, the glossopharyngeal nerve relays general sensations from the pharyngeal walls. However, in the case of burning mouth syndrome, the specific nerve responsible for transmitting pain in the tongue is CN V3 (lingual).