Question

O valor de x na equação (0,25)^-2x=√32 é:

a)-5/8 b)-1/2
c)5/8 d)5/4
e)1/2

Answer 1

$(\frac{25}{100})^{-2x} = 32^{1/2} \\ \\ ( \frac{100}{25} )^{2x} = (2^5)^{1/2} \\ \\ (4)^{2x} =2^{5/2} \\ (2^2)^{2x} = 2^{5/2} \\ 2^{4x} = 2^{5/2} \\ 4x= \frac{5}{2} \\ x = \frac{5}{8}$

Alternativa C

Answer 2

raiz de 32 é igual a: 2^5.1/2 = 2^5/2
(0,25)^-2x = (1/4)^-2x = (4)^2x = 2^4x
assim, temos:
2^5/2 = 2^4x
4x=5/2
x=5/8
Letra C