Diferentes abordagens para o estudo das funções exponenciais e logarítmicas

• Ano de defesa: 2016
• Autor(a) principal: Piano, Cátia
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Tecnológica Federal do Paraná; Pato Branco; Brasil; Mestrado Profissional em Matemática em Rede Nacional; UTFPR
• Palavras-chave em Português: Matemática - Estudo e ensino; Funções exponenciais; Logarítmos; Mathematics - Study and teaching; Exponential functions; Logarithms; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.utfpr.edu.br/jspui/handle/1/1982

Along this work we search to better understand the exponential and logarithmic functions so that we could present them differently from the traditional approach. In a first moment we recovered the concepts of potentiation, from the natural exponents, through the entire rational exponents, to the real exponents and then defining the logarithm as the ”reverse operation”of potentiation. Then we characterize the exponential function through basic properties (be monotonous and take sums into products) and define the logarithm as its inverse function. After that, we did the same with the logarithmic function, defining it through basic properties (being increasing and taking products into sums) and then defining the exponential function as its inverse, showing, finally, that both ways of defining the exponential functions and, consequently, the logarithmic functions, are equivalent. Finally, we bring a geometric characterization of the logarithms, making the demonstrations of properties more intuitive and simple.