Question

Sabendo que *log 2 =m, log 3 =n e log 5 =p, calcule os seguintes logaritmos em função de m, n e p a) log 60: b) log 243: c)log 7,5: d) (log60 + log 7,5) /7

Answer 1

a) log 60 = log (4•3•5) = log4 + log3 + log5 = log2^2 + n + p = 2log2 + n + p = 2m + n + p

b) log243 = log 3^5 = 5log3 = 5n

c) log7,5 = log (15/2) = log15 - log2 = log(3•5) - m = log3 + log5 - m = n + p - m

d) (log60 + log7,5) / 7 = (2m+n+p+n+p-m) / 7 = (m + 2n + 2p)/7