Understanding logarithms: What are the difficulties that students have?

Calculus, linear algebra, and differential equations are more complex areas of mathematics, and students may have difficulty moving forward in these courses due to their difficulties with logarithms. In order to help students succeed in mathematics and related fields in the long run, it is crucial to identify and resolve these obstacles in higher education. The aim of this thesis is to investigate the challenges high school students in Baku, Azerbaijan, face in understanding logarithms, crucial for success in advanced mathematics and related disciplines. It examines the relationship between students' performance on logarithmic tasks and teachers' perceptions of their understanding and abilities. The research reveals that students' difficulties primarily stem from a lack of foundational mathematical skills and a deep conceptual understanding of logarithms. The study employs a mixed-methods approach, combining thematic analysis of teacher interviews with descriptive statistical analysis of student assessments. Errors in student responses are categorized according to Gagné’s taxonomy, highlighting common cognitive challenges. The findings emphasize the need for educational strategies that enhance students' understanding and application of logarithms, aiming to foster their long-term academic success.