Question

Considerando as aproximações log 2 = 0,3 e log 3 = 0,48, calcule: log de raiz quinta de 90

Answer 1

$log \sqrt[5]{90} = \\\\ log90^{\frac{1}{5}} = \\\\ \frac{1}{5} \cdot log9 \cdot 10 = \\\\ \frac{1}{5} \cdot ( log3^{2} +log10) = \\\\ \frac{1}{5} \cdot (2log3+log10) = \\\\\ \frac{1}{5} \cdot (2 \cdot 0,48+1) = \\\\ \frac{1}{5} \cdot 1,96 = \frac{1,96}{5} = \boxed{\boxed{0,392}}$