Try to find patterns. Look at the two parts of the word (eu and logy) and then find patterns in the examples given.
All 3 of the examples with eu in them have something to do with good or happiness.
All 3 of the examples with log in them have to do with some kind of talk or story.
So a eulogy is likely a good speech or a pleasant speech. And that's pretty much what a eulogy is - a speech that people give at funerals praising someone's good qualities.