There are a plethora of synonyms for the phrasal verb "put account". Some of the common alternatives for this idiom include "make a record", "list", "enter", "register", "log", "note down", "keep track of", "document", "chronicle", "narrate", "describe", and "report" among others. Each of these words carries a slightly different connotation, and the choice of the particular synonym depends on the context and the intended audience. Whether it is for bookkeeping, writing an essay, or simply communicating information, these different ways of expressing the idea of "putting an account" offer a rich and varied vocabulary for clear and effective communication.