Question

me ajudem nessa quest ao de logaritimo, por favor.

Answer 1

$log \frac{1}{2} (\sqrt[n]{32}) = \frac{1}{n} . log \frac{1}{2} 32 = \frac{1}{n} . (-5) = - \frac{5}{n}$

$log \frac{1}{2} (8^{n+2}) = (n+2) . log \frac{1}{2} 8 = (n+2).(-3) = -3(n+2)$

$M \frac{log \frac{1}{2} \sqrt[n]{32}}{log \frac{1}{2} 8^{n+2}} = M \frac{- \frac{5}{n} }{-3(n+2)} = M \frac{5}{3n(n+2)} = \frac{5}{3} . M \frac{1}{n(n+2)} =$

$\frac{5}{3} . [ \frac{1}{3} \frac{1}{8} \frac{1}{15} \frac{1}{24} ] = \frac{5}{3} . \frac{40+15+8+5}{120} = \frac{5}{3} . \frac{68}{120} = \frac{5}{3} . \frac{17}{30} = \frac{17}{18}$