Question

Dado log²=0,30 e log³=0,48. Quando vale:

A)log 0,0006 B)log 14,4

C)log 250 D)log 20

Answer 1

Resposta:

a)

$log0,0006 = log \frac{6}{10000} = log6 - log10000 = log(2.3) - 4 = log2 + log3 - 4 = 0,30 + 0,48 - 4 = - 3,22$

b)

$log(14,4) = log( \frac{144}{10} ) = log144 - log10 = log(3.3.2.2.2.2) - 1 = 2 log3 + 4 log2 - 1 = 2.0,48 + 4.0,30 - 1 = 0,96 + 1,2 - 1 = 1,16$

c)

$log250 = log(25.10) = log25 + log10 = log {5}^{2} + 1 = 2. log( \frac{10}{2} ) + 1 = 2.( log10 - log2) + 1 = 2.(1 - 0,30) = 2.0,7 = 1,4$

d)

$log20 = log(2.10) = log2 + log10 = 0,30 + 1 = 1,3$