Dilemmas in solving one type of exponential equations in mathematics teaching - Marković Olivera R.; Zubac Marina A. (Zbornik radova (Univerzitet u Kragujevcu. Pedagoški fakultet u Užicu))
In this paper we considered the problem of solving equations of the form f ( x ) a(x^ = f ( x ) h(x), ie. exponential equations in which the unknown is both in the base and the exponent. We analysed how solving these so-called powerexponential equations shown in textbooks and collections of math problems for the second grade of vocational schools and grammar schools, as well as in some collections of math problems intended for the preparation of the entrance exam at technical faculties in the Republic of Serbia. We realised that in these textbooks there are two approaches to these equations, which results in obtaining different sets of solutions. Namely, in some collections of math problems the starting point is the fact that the real solutions to an equation are all real numbers for which the given equation becomes an exact equality, including those real numbers for which the base f(x) is a negative number, while in others the possibility of a negative base is excluded due to the area of definition of the function y = f ( x ) a(x). Obtaining different sets of solutions is a problem for both students and teachers because they do not know which approach is correct and which set of solutions is correct. In the paper, we also indicated a possible solution to this problem.