Question

(4^x)^2 = 16 vezes 2^x², o valor de x elevado à x é:

a) 27
b) 4
c) 1/4
d) 1
e) -1/27

Answer 1

$(4^x)^2 = 16.2^{x^2} \\ \\ 4^{2x} = 2^4 . 2^{x^2} \\ \\ (2^2)^{2x} = 2^{x^2 + 4} \\ \\ \not2^{4x} = \not2^{x^2 + 4} \\ \\ x^2 - 4x + 4 = 0 \\ \\\Delta = 16 - 4*4 \\ \\ \Delta = 0 \\ \\ x = \dfrac{4}{2} \\ \\ \boxed{x = 2} \therefore x^x = 2^2 = 4$

Alternativa "B"