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A tax that the city could levy against a real estate brokerage firm, based on its gross receipts, would be:

  1. a business license tax.

  2. a documentary tax stamp.

  3. a sales tax.

  4. a use tax.

The correct answer is: a business license tax.

A business license tax is a fee that many cities and municipalities impose on businesses operating within their jurisdiction. This tax is typically based on the gross receipts of the business, which means that the amount the business has earned in revenue influences the tax amount owed. Real estate brokerage firms, as businesses, are subject to this type of tax because they generate income through their services in the real estate market. Other options do not align with the nature of the question. A documentary tax stamp is commonly associated with the transfer of real property and is typically used in real estate transactions, rather than imposed on the gross receipts of a business. A sales tax is levied on the sale of goods and services transferred to consumers, not specifically on a brokerage's gross receipts. Similarly, a use tax relates to the use of goods and not to a business's revenue, so it does not apply directly to a brokerage firm’s income. Thus, the business license tax is the correct answer that fits the context provided in the question.