I gave you the definition from Strong's.
Note on "acknowledge" in Philippians 2:11
S1843 eksomologéō (from 1537 /ek, "wholly out from," intensifying 3670 /homologéō, "say the same thing about") – properly, fully agree and to acknowledge that agreement openly (whole-heartedly); hence, to confess ("openly declare"), without reservation (no holding back).
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ἐξομολογέω (s. next entry and ὁμολογέω) 1 aor. ἐξωμολόγησα; fut. mid. ἐξομολογήσομαι; aor. mid. ἐξωμολογησάμην LXX (quotable since III B.C.—Mitt-Wilck. II/2, 20, 18; 37, 17—PHib 30, 18 [300–271 B.C.]; also LXX, pseudepigr., Philo, Joseph.).
① to indicate acceptance of an offer or proposal, promise, consent, act., abs. Lk 22:6 (the act. is found as rarely [perh. Alex. Aphr., An. Mant. II 1 p. 168, 15] as the pass. [perh. SIG 685, 95]).
② to make an admission of wrong-doing/sin, confess, admit, mid. (Plut., Eum. 594 [17, 7], Anton. 943 [59, 3] τ. ἀλήθειαν, Stoic. Repugn. 17 p. 1042a; Sus 14; Jos., Bell. 1, 625, Ant. 8, 256) τὶ someth. (POslo 17, 14 [136 A.D.] τὸ ἀληθές; Cyranides p. 100, 18 πάντα ὅσα ἔπραξεν; Orig., C. Cels. 2, 11, 30 τὸ ἡμαρτημένον) τὰς ἁμαρτίας (Jos., Ant. 8, 129; s. the ins in Steinleitner, nos. 13, 5; 23, 2; 24, 11; 25, 10) Mt 3:6; Mk 1:5 (cp. 1QS 1:24–26); Js 5:16 (s. PAlthaus, Zahn Festgabe 1928, 1ff); Hv 1, 1, 3; Hs 9, 23, 4. τὰς ἁ. τῷ κυρίῳ confess sins to the Lord Hv 3, 1, 5, cp. 6. τὰ παραπτώματα ἐν ἐκκλησίᾳ confess transgressions in the congregation D 4:14. περὶ τῶν παραπτωμάτων make a confession of transgressions 1 Cl 51:3. ἐπὶ τ. ἁμαρτίαις for sins B 19:12. Abs. make a confession of sins Ac 19:18; 2 Cl 8:3. W. dat. of the one to whom sins are confessed 1 Cl 52:1, 2 (w. similarity in form to Ps 7:18; 117:19 and sim. Ps passages, but not=praise because of 1 Cl 51:3 [s. 4 below]).—JSchnitzer, D. Beichte im Lichte d. Religionsgesch.: Ztschr. f. Völkerpsychol. 6, 1930, 94–105; RPettazzoni, La confessione dei Peccati II ’35.
③ to declare openly in acknowledgment, profess, acknowledge, mid. (PHib 30, s. above; POxy 1473, 9; Lucian, Herm. 75) w. ὅτι foll. Phil 2:11 (Is 45:23; s. 4 below).—Nägeli 67.
④ fr. the mngs. ‘confess’ and ‘profess’ there arose, as Rtzst., Erlösungsmyst. 252 shows, the more general sense to praise, in acknowledgment of divine beneficence and majesty (so mostly LXX; TestJob 40:2 πρὸς τὸν πατέρα ) w. dat. of the one praised (oft. LXX; TestSol 1:5; Philo, Leg. All. 1, 80) σοί (2 Km 22:50; 1 Ch 29:13; Ps 85:12; 117:28 al.; Did., Gen. 60, 20) Mt 11:25=Lk 10:21 (s. Norden, Agn. Th. 277–308; JWeiss, GHeinrici Festschr. 1914, 120ff; TArvedson, D. Mysterium Chr. [Mt 11:25–30] ’37; NWilliams, ET 51, ’40, 182–86; 215–20; AHunter, NTS 8, ’62, 241–49); Ro 15:9 (Ps 17:50); 1 Cl 26:2; 61:3; B 6:16 (cp. Ps 34:18). τῷ θεῷ (Tob 14:7; Philo, Leg. All. 2, 95) Ro 14:11 (Is 45:23); τῷ κυρίῳ (fr. Gen 29:35 on, oft. in LXX) 1 Cl 48:2 (Ps 117:19); Hm 10, 3, 2.—DELG s.v. ὁμός. M-M. EDNT. TW. Sv.
Arndt, W., Danker, F. W., & Bauer, W. (2000). A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed., p. 351). Chicago: University of Chicago Press.
Links to BDB and BAGD lexicons online.
https://archive.org/details/BDBHebrewLexicon
http://lareopage.free.fr/a&g/main.htm