Logarithmic risk and safety incidence indices for application in the risk assessment for a large population that is subjected to some forms of common hazards such as disease or natural disasters, are introduced. For a limited size population, more appropriate likelihood indices are derived for the comparison of hazardous activities that are peculiar to a small population that is engaged in a hazardous or other societal activity. The approach possesses a large domain of applicability. It matches intuition and provides a measurement of the levels of safety or risk on a logarithmic scale. Every unit increase in the incidence Safety Index corresponds to a Risk decrease by a factor of 10. The risk and safety indices sum up to a value of 10. Their values are defined over the interval [0, 10]. As illustrations, the methodology is applied to the analysis of the hazardous activities in a large population, the Beaufort wind scale as relevant in the monitoring and control of wind turbines, and to the unemployment situation from the local, regional and national perspectives. Useful insights for the allocation of resources, remedial actions, monitoring, and control strategies can be deduced from the proposed indices than from just the row data.