Methods for solving logarithmic inequalities

One of the difficult topics considered in the tasks of the unified state exam in mathematics at the profile level is the topic "Logarithmic inequalities". The paper presents non-standard methods for solving these problems: the graphical method, the interval method, the rationalization method, the variable replacement method, and the majorant method. Each technique is demonstrated with specific examples. The article provides recommendations for choosing a method for solving logarithmic inequalities. A well-chosen method can significantly facilitate, and in some cases speed up the process of finding a solution.