Question

Calcule os seguintes logaritmos:

a- Sendo ㏒ 2 = 0,30 e㏒ 3 = 0,47, calcule ㏒6000;

b- Sendo㏒ 2 = 0,301 e㏒ 7 = 0,845, qual será o valor de ㏒ 2800;

c- Se ㏒ 2 = x e ㏒ 3 = y, calcule log 37,5;

d- Calcule a expressão ㏒ 2/3 + log 3/4 +㏒ 4/5 - ㏒ 14/55

Answer 1

$A:\\\log600 = \log(2.3.100) = \log2+\log3+\log100 = 0,3 +0,4 + 2 = 2,7\\B:\\\log2800 = \log(2^2.7.100) = 2\log2 + \log7+\log100 = 3,447\\C:\\\log37,5 = \log\frac{750}{20} = \log750-\log20 =\log(2.250)=\log2+\log250-\log20=\\\\(\log5^3.2)-\log(2.10)+x= \log5^3+\log2-\log2-\log10+x = \log5^3+x+x-x-1= \\\\\log5^3+x-1=3\log5+x-1$