Question

Sendo log 2 = 0,3, log 3 = 0,4. calcule:
log 2000​

Answer 1

Neste exercício, vamos utilizar a fatoração e as propriedades dos logaritmos.

$\log2000~=\\\\\\\underline{Fatorando}~o~logaritmando~(2000)\\\\\\=~\log\,(2\cdot10\cdot10\cdot10)\\\\\\Aplicando~a~propriedade~do~\underline{logaritmo~do~produto}\\\\\\=~\log2~+~\log10~+~\log10~+~\log10\\\\\\Logaritmo~com~logaritmando~e~base~iguais~\acute{e}~igual~a~1,~logo:\\\\\\=~\log2~+~1~+~1~+~1\\\\\\Substitundo~o~valor~de~\log2\\\\\\=~0,3~+~1~+~1~+~1\\\\\\=~\boxed{3,3}$

Resposta:  3,3