Question

Dados log 2 = 0,30, log 3 = 0,48, log 5 = 0,70 e log 7 = 0,85, quanto vale:

a)log 25
b)log 40
c)log 27
d) 14,4
e)log3 15

Answer 1

a) log25 = log5² = 2log5 = 2 * 0,7 = 1,4

b) log40 =
log2² . 10 =
2log2 + log10 = 2 * 0,3 + 1 = 0,6 + 1 = 1,6

c) log27 = log3³ = 3log3 = 3 * 0,48 = 1,44

d) log14,4 =
log144/10 = 
log144 - log10 =
log(2⁴ . 3²) - log10 = 
log2⁴ + log3² - log10 =
4log2 + 2log3 - log10 =
(4*0,30) + (2*0,48) - 1 = 1,2 + 0,96 - 1 = 1,16

e) log3 15 =
log15/log3 = 
(log3 . 5) / (log3) = 
(log3 + log5) / log3 = 
(0,48 + 0,7) / 0,48 = 1,18 / 0,48 = 2,46