Question

(pucrj 2015) Se log1/2 x= -3, então raiz cúbica de x + x^2 vale: a) 3/4 b) 6 c) 28 d) 50 e) 66

Answer 1

Olá!

Da definição de logaritmos, tiramos que:

$\\ \displaystyle \mathsf{\log_{\frac{1}{2}} x = - 3} \\\\\\ \mathsf{\left ( \frac{1}{2} \right )^{- 3} = x} \\\\\\ \mathsf{x = \left ( \frac{2}{1} \right )^3} \\\\\\ \boxed{\mathsf{x = 8}}$


 Com efeito,

$\\ \displaystyle \mathsf{\sqrt[3]{\mathsf{x}} + x^2 =} \\\\ \mathsf{\sqrt[3]{\mathsf{8}} + 8^2 =} \\\\ \mathsf{2 + 64 =} \\\\ \boxed{\boxed{\mathsf{66}}}$