The article discusses examples of solving exponential inequalities by the inverse action method, as well as a rationalization method that simplifies the solution of exponential inequalities. The purpose of considering these methods is the development of logical thinking in solving mathematical problems. When solving problems, you need good knowledge of theoretical material and the ability to use it, mastery of general approaches to solving problems, and experience in solving exponential inequalities. The process of solving significant inequalities develops creative activity and shapes logical thinking. Logical thinking develops in students the skills of critical perception of the world around them, the desire to understand the causes and essence of the most diverse concepts and phenomena, contributes to academic success.