Question

Qual é a resposta desta questão?

Log_{0.2} \sqrt[3]{25}

Answer 1

$Log_aB=c \quad\to\quad a^c= B \\ \\ Log_{0.2}\ \sqrt[3]{25} = x \quad \to \quad (0,2)^x= \sqrt[3]{25} \\ \\ \\ Log_{0.2}\ \sqrt[3]{25} = x \quad \to \quad ( \frac{2}{10})^x= \sqrt[3]{5^2} \\ \\ \\ Log_{0.2}\ \sqrt[3]{25} = x \quad \to \quad ( \frac{1}{5})^x= 5^ { \frac{2}{3}} \\ \\ \\ Log_{0.2}\ \sqrt[3]{25} = x \quad \to \quad ( \frac{1}{5})^x= \frac{1}{5}^ {- \frac{2}{3}} \\ \\ \\ Log_{0.2}\ \sqrt[3]{25} = x \quad \to \quad \boxed{x= - \frac{2}{3} }}$