Question

O valor de x que verifica a equação $\sqrt{ 4^{x+1} } = \frac{1}{ 16^{x+1} } é :$ é

Answer 1

$\sqrt{4^{x+1}} = \frac{1}{16^{x+1}} \\\\ (4^{x+1})^{\frac{1}{2}}= (16^{x+1})^{-1} \\\\ 4^{\frac{x}{2}+\frac{1}{2}} = (4^{2})^{-x-1} \\\\ \not 4^{\frac{x}{2}+\frac{1}{2}} = \not 4^{-2x-2} \\\\ \frac{x}{2}+\frac{1}{2} = -2x-2 \\\\ \frac{x}{2}+2x = -2-\frac{1}{2} \ \ \times 2 \\\\ x+4x = -4-1 \\\\ 5x = -5 \\\\ \boxed{\boxed{x = -1}}$

$\boxed{\boxed{S = \{-1\}}}$

Alternativa A.

Answer 2

4^(x+1)/2 =  16^ -(x+1)

(2^2)^(x+1)/2 =  (2^4)^ -(x+1)

2^2(x+1)/2 =  2^-4(x+1)

2(x+1) =  -4(x+1)
     2

x + 1 =  - 4x - 4 

x + 4x = - 4 - 1

5x = - 5

x = - 1   letra A