Question

Se a=log3 5/log3 2, b=log5 10 e c=log5 5/2, o produto (a.b.c) é igual a: resposta log2 5 - log5 2.

Answer 1

a = log3 5/log3 2
b = log5 10
c = log5 5/2

Vamos aplicar duas propriedades:

1) logc a/logc b = logb a
2) logc a.logc b = logb a

a.b.c = (log3 5/log3 2).(log5 10).(log5 5/2)

a.b.c = (log2 5).(log5 10).(log5 5 - log5 2)

a.b.c = (log2 5).(log5 10).(log5 5) - (log5 10).(log5 2)

a.b.c = (log2 5).(log5 10) - (log5 10).(log5 2)

a.b.c = (log2 5) - (log5 2)

a.b.c = log2 5 - log5 2

Espero ter ajudado.