leave out or leave someone/ something out means omit it, not include it (e.g. Ann was left out of the side because she has been working very hard recently. We have to leave the sugar out of this receipt for the good health.)

let somebody down means disappoint by failing to keep a promise (e.g. You can always rely on your parents. So, you won't let them down, will you?)

let somebody/ something in means allow to enter or to allow water, light or air into something which is normally sealed. (e.g. Can you let the cat in before I go to my company? I need some new jacket for winter. These let water in.)

log in/ on means sign in (e.g. I can't log in to bank account because I've forgotten my password.)

log out/ off means sign out (e.g. If you don't log off your bank account on your computer then somebody could get your money.)

look after somebody/ something means take care of, or be in charge of (e.g. I have to look after my sick grandmother.)

look back (on something) means think about what happened in the past (e.g. My first job was in a project management. I didn't like it very much at the time but, looking back on it, I learned a lot and it was a very useful experience.)

look down on somebody means think less of, consider inferior, or have a low opinion of (e.g. I think they look down on me because I am not successful, but I look down on colleagues because I am better than they are.)

look for somebody/ something means try to find, or to investigate, or examine (e.g. I'm looking for a red dress for the wedding but I can't find them anywhere.)

look forward to means be excited and happy about something that is going to happen about the future (e.g. Are you looking forward to your holiday? I am looking forward to seeing you soon.)

look into something means investigate the facts about problems (e.g. We are going to look into the possibility of earnings as profits more than double.)

look out means be careful, or said or shouted in order to tell someone that they are in danger (e.g. Look out! you're going to drop that!)

look out for somebody/ something means take care of someone (e.g. I'm just trying to look out for you.)

look something over means quick check, examine (e.g. Can you look over my essay for spelling mistakes, when you have a few minutes?)

look up means to improve or become better (e.g. I hope things will start to look up in the new year.

look something up means search and find information in a dictionary or database etc. (e.g. If you don't know the meaning of a word, you can look it up in a dictionary.)

look up to somebody means have a lot of respect for (e.g. Every student in the class should look up to the teacher.)