The Formation of Skills for Solving of Logarithmic and Exponential Inequalities in Learning Algebra and the Foundations of Mathematical Analysis

Relevance: 1. the Topic is classical and traditional, it is reflected in almost all textbooks, it is given a lot of sources, so they are, of course, in all types of certification tests (use, University exams). 2. Exponential and logarithmic inequalities have existed for at least half a century, during which time they have become firmly embedded in the content of mathematical education, and they are traditionally one of the most complex. The question always arises how to develop skills for solving exponential and logarithmic inequalities? The relevance of the research is due to the contradiction between the classic traditional and strong entry of this topic into modern mathematical education and the openness of many problems in the formation of solving skills exponential and logarithmic inequalities. Goal: to develop guidelines for the study of logarithmic and exponential inequalities in high school. Tasks: * provide historical information about the occurrence of logarithms; consider the problems that lead to the solution of exponential and logarithmic inequalities; * find out what place the study of this topic occupies in the course of algebra and math- statistical analysis; * study the content and organization of training in solving logarithmic and educational inequalities in the high school curriculum; ∙ to analyze the changes in the level of complexity and logarithmic indicator- in the past 60 years, there have been many different types of inequality offered in exams; * conduct a logical and didactic analysis of this topic in the textbooks of Kolmogorov A. N., Mordkovich A. G., Vilenkin N. Ya., Nikolsky S. M., Alimov A. sh. and Merzlyak A. G.; * develop a special course program "logarithmic and exponential inequalities" for high school students; Object of research: learning process for solving logarithmic and exponential inequalities. Research methods: analytical, empirical, study and generalization of pedagogical experience.