Question

Quanto é Log de 64 na raiz cubica de 16 na base 1/4

Answer 1

$\\\\\frac{1}{4}=\frac{1}{2^2}=2^{-2}\\\\\\\log _\frac{1}{4} \left( 64\sqrt[3]{16} \right)=y\\\\(\frac{1}{4} )^y=64\sqrt[3]{16}\\\\(2^{-2})^y=64\sqrt[3]{16}\\\\2^{-2y}=64\sqrt[3]{16}\\2^{-2y}=2^6\sqrt[3]{16}\\\\2^{-2y}=\sqrt[3]{(2^6)^3(2^4)}\\2^{-2y}=\sqrt[3]{(2^{18})(2^4)}\\2^{-2y}=\sqrt[3]{2^{22}}\\\\2^{-2y}=(2)^{\frac{22}{3}}\\-2y=\frac{22}{3}\\-6y=22\\\boxed{y=\frac{-22}{6}=\frac{-11}{3}}$