Question

calcule o valor da expressao log $\sqrt[3]{100} . \sqrt[6]{0,1} - log 1000$

Answer 1

Aplicando propriedades de potencias e raízes

$\sqrt[3]{100} . \sqrt[6]{0,1} -log1000 \\ \\ = (10^{2} ) ^{ \frac{1}{3} }. (10^{-1}) ^{ \frac{1}{6} } -3 \\ \\=10 ^{ \frac{2}{3} -\frac{1}{6} } -3 \\ \\ = 10^{ \frac{3}{6} } -3 \\ \\ = 10^{ \frac{1}{2} } -3 \\ \\ = \sqrt{10} -3$