Question

log 50 + log 40 + log 20 + log 2,5 é igual a:


a) 1 b) 3 c) 5 d) 10 e) 100

Answer 1

log50 + log40 + log20 + log2,5 =

log50 + log40 + log20 + log(5/2) =

log50 + log40 + log20 + log5 - log2 =

log5*10 + log4*10 + log2*10 + log5 - log2 =

log5 + log10 + log4 + log10 + log2 + log10 + log5 - log2 =

Como log10 = 1

log5 + 1 + log2² + 1 + log2 + 1 + log5 - log2 =

2log5 + 2log2 + log2 - log2 + 3 =

2log5 + 2log2 + 3 =

2(log5 + log2) + 3 =

Voltamos a log5 + log2 = log(5*2) = log10

2log10 + 3 =

2 + 3 = 5 (letra c)