Question

Se log de x na base 4 mais log de x na base 16 é igual a 2.5. Então o valor de x é: *

Answer 1

$log_{4}(x) + log_{16}(x) = 2.5 \\ log_{4}(x) + \frac{ log_{4}(x) }{ log_{4}(16) } = 2.5 \\ log_{4}(x) + \frac{ log_{4}(x) }{2 } = 2.5\\ 2 log_{4}(x) + log_{4}(x) = 5 \\ 3 log_{4}(x) = 5 \\ log_{4}(x) = \frac{5}{3} \\ {4}^{ \frac{5}{3} } = x \\ x = \sqrt[3]{ {2}^{9} \times 2 } \\ x = \sqrt[3]{ {2}^{9} } \times \sqrt[3]{2} \\ x = {2}^{3} \times \sqrt[3]{2} \\ \boxed{x = 8 \sqrt[3]{2}}$