Question

Se log1/2X= -3 (log de X na base meio), então raiz cúbica de x + x^2 vale
a) 3/4
b) 6
c) 28
d) 50
e) 66

Answer 1

Vamos começar determinando o valor de "x".

$\log_{_{\frac{1}{2}}}x~=\,-3$

Aplicando a definição de logaritmo, temos:

$x~=~\left(\dfrac{1}{2}\right)^{-3}\\\\\\x~=~\left(\dfrac{2}{1}\right)^{3}\\\\\\x~=~\dfrac{2^3}{1^3}\\\\\\\boxed{x~=~8}$

Podemos agora calcular o valor da expressão:

$\sqrt[3]{x}~+~x^2~=\\\\\\=~\sqrt[3]{8}~+~8^2\\\\\\=~2~+~64\\\\\\=~\boxed{66}~~\rightarrow~Letra~E$