Question

sendo log 2= 0,301 log 3=0,477 log 5= 0,699 calcule: log 60

Answer 1

Vamos resolver este exercício utilizando a fatoração e as propriedades dos logaritmos.

$\underline{Fatorando}~o~logaritmando\\\\\\\log60~=~\log\,(2\cdot2\cdot3\cdot5)\\\\\\Aplicando~a~propriedade~do~\underline{logaritmo~do~produto}\\\\\\\log60~=~\log2~+~\log2~+~\log3~+~\log5\\\\\\\underline{Substituindo}~os~valores~dos~logaritmos~conhecidos\\\\\\\log60~=~0,301~+~0,301~+~0,477~+~0,699\\\\\\\log60~=~0,602~+~0,477~+~0,699\\\\\\\log60~=~1,079~+~0,699\\\\\\\boxed{\log60~=~1,778}$