look up

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US /lʊk/ 
UK /lʊk/ 

Longman Dictionary of Contemporary English

look up

look up phrasal verb (see also look)
 1. if a situation is looking up, it is improving SYN improve, get better:
   • Now the summer’s here things are looking up!
 2. look something ↔ up if you look up information in a book, on a computer etc, you try to find it there:
   • Look the word up in your dictionary.
   • I’ll just look up the train times.
 3. look somebody ↔ up to visit someone you know, especially when you are in the place where they live for a different reason:
   • Don’t forget to look me up when you come to Atlanta.

Oxford Advanced Learner's Dictionary

look up

 

I.ˌlook ˈupderived

 

(informal) (of business, sb's situation, etc.) to become better

Syn:  improve

• At last things were beginning to look up.

Main entry: lookderived

II.ˌlook ˈup (from sth)derived

 

to raise your eyes when you are looking down at sth

• She looked up from her book as I entered the room.

Main entry: lookderived

Cambridge Advanced Learner's Dictionary

look up

look up (IMPROVE) phrasal verb INFORMAL
to become better:
I hope things will start to look up in the new year.
Our financial situation is looking up at last.

Collins Advanced Learner’s English Dictionary

look up

 1) PHRASAL VERB If you look up a fact or a piece of information, you find it out by looking in something such as a reference book or a list.
  [V n P] I looked your address up in the personnel file...
  [V P n (not pron)] Many people have to look up the meaning of this word in the dictionary.
 2) PHRASAL VERB If you look someone up, you visit them after not having seen them for a long time.
  [V n P] I'll try to look him up, ask him a few questions...
  [V P n (not pron)] She looked up some friends of bygone years.
  Syn:
  visit
 3) PHRASAL VERB: usu cont If a situation is looking up, it is improving. [INFORMAL]
  [V P] Things could be looking up in the computer industry.
  Syn:
  improve