Question

Dados log 2 = 0,30 //// log 3 = 0,48 /////////

Log de 75 na base 3 é: ?????

Answer 1

Fatore o 75 para usar o log 2 e o log 3.

75 = 3.5²

Transformando log de 75 na base 3 para base 10:

[] = base
log[3] 75 = log 75 / log 3

log[3] 75 = log 3.5.5/ log 3
log[3] 75 = log 3+2(log 5) / log 3
log[3] 75 = log 3 +2( log 10/2) / log 3
log[3] 75 = 0,48 + 2(0,7) / 0,48
log[3] 75 = 1,88/0,48
log[3] 75 = 3,91