Question

2. Sendo 2 = 10^0,301 ; 3 = 10^0,477 e
5 = 10^0,699, determine o
logaritmo decimal de:
a)36
b)30
c) 1801​

Answer 1

log 36 = 2log 6 = 2[(log 2 + log 3)]  

b)  

log 30 = log 3 - log 10  

c)  

log 180 = log 18 + log 10  

= log 3 + log 6 + log 10  

=log 3 +log 2 +log 3 +1  

=2log 3 + log 2 + 1  

Propriedades dos Logarítimos  

log[a] b = x => b=a^x ->[a] é a base  

log(a) b=log b/log a ==>mudança de base  

log a/b=log a-log b  

log a*b=log a+log b  

b*log a= log a^b  

(1/b)*log a= log a^(1/b)  

log 10 =1, pois 10^1=10  

log 5= log10/2=log 10 - log 2=1-log 2  

log a = - colog a