Exegesis:

to de paidion ēuxanen kai ekrataiouto pneumati ‘the child grew up and became strong in spirit’; the imperfect tense of the verbs expresses the process of growing and becoming strong.

auxanō ‘to grow,’ both transitive and intransitive.

krataioō (also 2.40) ‘to strengthen,’ in the passive ‘to become strong.’

pneumati either ‘in (his own) spirit’ (most commentators and translators) or ‘in the (Holy) Spirit’ (Plummer, cf. Williams, An American Translation, Moffatt); the former interpretation is to be preferred. The dative is metaphorically local, cf. Moule 44, 46.

kai ēn en tais erēmois ‘and he was in the desert.’

hai erēmoi, scil. chōrai ‘the desert regions.’

heōs hēmeras anadeixeōs autou pros ton Israēl ‘till the day of his appearing before Israel.’

anadeixis ‘commissioning,’ ‘installation’ or ‘public appearance,’ preferably the latter.

Translation:

Grew. The verb is often rendered analytically, e.g. ‘to become big’ (Apache), ‘his-bigness rose/increased’ (Javanese), or a term built on the word ‘big,’ and expressing the concept of increase by reduplicating that word (Toraja-Sa’dan).

Became strong in spirit. The two last words qualify “strong”: ‘was-made-strong as to his soul’ (Sundanese), ‘became spiritually strong,’ “gathered spiritual strength” (The Four Gospels – a New Translation). In Ekari a literal rendering would result in ‘became hard-hearted,’ i.e. ‘stubborn’; therefore the phrase had to be rendered ‘became wise in his consciousness.’ For similar reasons Tboli uses an adjective meaning ‘sturdy/steady/reliable,’ lit. ‘nailed.’ Spirit, or, ‘character’ (Tboli, using a derivation of ‘breath-of-life’), ‘heart’ (Vai, where a literal rendering of ‘spirit’ would suggest that John had so strong a ghost as to be able to live on some time after his death), ‘consciousness’ (Ekari, a compound of ‘thought’ and ‘speech’); and cf. above on v. 47.

Till the day of his manifestation, or as a verbal clause, ‘until (the day) he showed/made-publicly-known himself’ (Navajo, Apache, Batak Toba), ‘up to the time that he appeared in public.’

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.