Question

Considerando as aproximações log 2 = 0,3 e log3 = 0,48, calcule o valor:

a) Log 0,05

b) log 3,6

c) log 2000

d) Log ( $\sqrt[5]{90}$ )

Answer 1

a) log 0,05 = log 5/100 = log 5 - log 100 =
log 10/2 - 2 = log 10 - log 2 - 2 = 1 - 0,3 - 2 = -1,3

b) log 3,6 = log 36/10 = log 36 - log 10 =
log 4·9 - 1 =log 2² + log 3² - 1 =
2·log 2 + 2·log 3 -1 = 2·0,3 + 2·0,48 - 1 = 0,56

c) log 2000 = log 2·1000 = log 2 + log 1000 =
0,3 + 3 = 3,3

d) log 90^√5 = √5·log 90 = √5·log 10·9 = √5·(log 10 + log 3²) = √5·(1+2·log 3) = √5·(1+2·0,48) = 1,96√5 ≈ 4,38