Question

s= log 0,001 na base 10 + log 3raiz de 3 na base 3 -log de 16 na base 8

Answer 1

Vou resolvendo utilizando as propriedades de logarítmo sem explicar, apenas fazendo os passos. Caso se perca, comente que explico.

$S = log0,001+log_{3}3\sqrt{3}-log_{8}16 \\\\ S = log10^{-3}+log_{3}3+log_{3}\sqrt{3}-(log_{2^{3}}2^{4}) \\\\ S = -3 \cdot (log10)+log_{3}3+log_{3}3^{\frac{1}{2}}-(\frac{1}{3} \cdot 4 \cdot log_{2}2) \\\\ S = -3+1+\frac{1}{2}-\frac{4}{3} \\\\ S = -2+\frac{1}{2}-\frac{4}{3} \\\\ MMC = 6 \\\\ S = \frac{-2 \cdot 6+3 \cdot 1-4 \cdot 2}{6} = \frac{-12+1-8}{6} = \boxed{\boxed{-\frac{19}{6}}}$