There are several synonyms that can be used for the phrase "put on one's account." Some of these synonyms include "charge to," "debit," "impute," "assign," and "log." All of these words refer to the act of recording an amount or expense to a specific account. "Charge to" and "debit" both suggest adding an amount to a financial record, while "impute" and "assign" imply assigning responsibility or blame to a certain account. "Log" refers to the act of keeping a record of all transactions, including those that are charged or debited to a specific account. Regardless of the synonym used, the concept of recording an amount to an account remains the same.