Autor: 1º Ano do Colégio Batista | Publicado: 2012-09-07T12:04:00-07:00

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A origem dos LOGARÍTMOS

&nbsp;&nbsp; É atribuído aos
babilônicos os primeiros vestígios do surgimento dos logaritmos.Existem
indícios de que babilônicos construíram tabelas logarítimicase que Arquímedes
eleborou citações que tiveram importância na elaboração dos conceitos iniciais
sobre logaritmos.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; John Napier e
Jobist Burgi foram dois grandes matemáticos muito importantes para as ideias
mais próximas do que se tem hoje sobre logarítmos

&nbsp; Napier não era
matemático profissional, mas realizava inúmeros trabalhos relacionados a vários
assuntos.Seus estudos foram primordiais no desenvolvimento dos logaritmos.E
Burgi era maatemático suíço e desenvolveu trabalhos relacionados com logaritmos
no mesmo período de Napier.

&nbsp; Os grandes trabalhos
publicados por Napier e Burgi &nbsp;&nbsp;contribuíram
para a facilidade e agilidade dos cálculos relacionados à astronomia,navegação
e comércio.Eles criaram tabelas que eram utilizadas no desenvolvimento das
expressões logarítmicas.

&nbsp;&nbsp; Os logaritmos
introduzidos por Napier utilizavam bases inadequadas, foi partindo dessa ideia
que Henry Briggs sugeriu a Napier a mudança dos logaritmos para uma base
decimal. Partindo dos estudos
de Napier, Briggs desenvolveu logaritmos na base decimal, construindo uma
tabela de logaritmos dos números de 1 a 1000. Henry Briggs foi responsável pela
introdução dos logaritmos na prática e da imensa vantagem em sua utilização.

Definição de Logarítmo

&nbsp;&nbsp; Na matemática o
logaritmo (do grego: logos=razão e arithmos=número), de base b, maior que zero
e diferente de 1, é uma função que faz corresponder aos objectos x a imagem y
tal que by=x. Usualmente é escrito como logb x=y.

&nbsp; Exemplos: 3 4=81,
portanto log3 81=4.

&nbsp;&nbsp; Ou seja, o
logaritmo é o expoente que uma dada base deve ter para produzir certa
potência.No exemplo anterior o logaritmo de 81 na base 3 é 4 é o expoente que a
base 3 deve usar para resultar 81.

Para cada
base (b em bn), existe uma função logaritmo e uma
função exponencial; elas são funções inversas Com bn = x:

Exponenciais determinam x
     quando dado n; para encontrar x, se multiplica b por b
     (n) vezes.
Logaritmos determinam n
     quando dado x; n é o número de vezes que x precisa
     ser dividido por b para se obter 1. Depois que seu logaritmo
     estiver dividido some novamente com o coeficiente e chegará a um resultado
     parcialmente correto.&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;


·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Exemplos:&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;1.&nbsp;&nbsp; log28 = 3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; porque&nbsp;&nbsp;&nbsp;
23 = 8&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2.&nbsp;&nbsp;
log71 = 0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
porque&nbsp;&nbsp;&nbsp; 70 = 1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
5.&nbsp;&nbsp;
log31/9 =-2&nbsp;
porque&nbsp;&nbsp;&nbsp; 3-2=1/9