When a license tax or fee is imposed in accordance with Section 45–44–244, it shall be unlawful for any person to engage in or follow any trade, occupation, or profession, as defined in this subpart, within the county, on and after the law day of such levy, without paying such license taxes or fees for the privilege of engaging in or following such trade, occupation, or profession. In cases where compensation is earned as a result of work done or services performed both within and without the county the license fees required under the ordinance or resolution shall be computed by determining upon the oath of the employer, or if required by the county director of revenue, upon the oath of the employee, that percentage of the compensation earned from the portion of the work which was done or performed within the county.