Curso de logaritmo para o ensino médio com proposta de atividades alternativas

Abstract

This work intends to address the teaching of logarithms and exponential and logarithmic functions by means of mathematical models that characterize them. We will use the arithmetic and geometric progressions as main points in understanding of exponential and logarithmic functions. We also recommend that before starting the study of these functions, make a brief study of those progressions, since this order may not be common in High School. Through problem situations, where the logarithmic function and its inverse, the exponential function, it is shown the most appropriate mathematical models, due to its specifications, we will show the main features, properties and definitions of these two functions. These problem situations will be given in proposed activities where we intend to show the development of the concepts and the logarithms properties in the course of time, exemplify the characterization of the logarithmic function and the exponential function and provide examples of everyday problems that are modeled by these functions. We will also use a spreadsheet, in one of the proposed activities, to show properties of the exponential and logarithmic functions and the important mathematical constant "e", which usually appears in natural phenomena. We will see that the initial reason of logarithms success, to increase computing power, lost ground nowadays, for computers and calculators. Currently, the reason that makes the logarithms continue to receive emphasis on the teaching of Mathematics is because the logarithmic function and the exponential function is the only way to describe the magnitude mathematically whose rate of variation is proportional to the quantity of that magnitude in a given moment.