Question

log8 2√2 (log de 2 raiz de 2 na base 8)

Answer 1

Resposta:

Vamos utilizar algumas propriedades dos logaritmos para resolver essa questão:

$log_{8} (2\sqrt{2}) = log_{2^{3}} (2\sqrt{2}) = \frac{1}{3}\,log_{2}(2\sqrt{2}) = \frac{1}{3}(log_{2}\,2 + log_{2}\,\sqrt{2}) = \frac{1}{3}(log_{2}\,2+log_{2}\,2^{\frac{1}{2}}) = \frac{1}{3}(log_{2}\, 2 + \frac{1}{2}\,log_{2}\,2) = \frac{1}{3}[log_{2}\,2(1 + \frac{1}{2})] = \frac{1}{3}[1(\frac{3}{2})] = \frac{1}{2}$