Question

Se log4 x= -2 , o valor de logx 4 é:
a) 3
b) -1,5
c) 0,5
d) -0,5
e) 1,5
f) 3

Answer 1

$log_{4}x = -2 \\\\ 4^{-2} = x \\\\ x = (\frac{1}{4})^{2} \\\\ \boxed{x = \frac{1}{16}} \\\\\\\\ log_{\frac{1}{16}}4 = y \\\\ (\frac{1}{16})^{y} = 4 \\\\ 16^{-1y} = 4 \\\\ (4^{2})^{-1y} = 4 \\\\ 4^{-2y} = 4^{1} \\\\ \not 4^{-2y} = \not 4^{1} \\\\ -2y = 1 \\\\ \boxed{\boxed{y = -\frac{1}{2}} \ ou \ \boxed{-0,5}}$


Alternativa D.

Answer 2

log x = - 2
    ⁴
4^(- 2) = x
(1/4)² = x
1/16 = x
x = 1/16

log 4
    x
log 4
  1/16
(1/16)^x = 4
16^(- x) = 4
(2⁴)^(- x) = 2²
2^(- 4x) = 2^2
- 4x = 2 . (- 1)
4x = - 2
x = - 2/4
x = - 1/2
x = - 0,5

Resp.: Alternativa "D".