Question

Sabendo que 16^(x+2) = 128^(x+1), calcule o valor de x³-2

Answer 1

16^(x + 2) = 128^(x + 1)

(2^4)^(x + 2) = (2^7)^(x + 1)

2^(4x + 8) = 2^(7x + 7)

4x + 8 = 7x + 7

7x - 4x = 8 - 7

3x = 1

x = 1/3

Calcular x³ - 2

(1/3)³ - 2 

1/9 - 2 = (1 - 18)/9 = -17/9

Resposta: - 17/9

Espero ter ajudado.

Answer 2

$16^{x+2} = 128^{x+1} } \\ \\ 2^{4(x+2)}= 2^{7(x+1)} \\ \\ 4(x+2)=7(x+1) \\ \\ 4x+8=7x+7 \\ \\ 4x-7x=7-8 \\ \\ -3x=-1 \\ \\ x= \frac{1}{3} \\ \\ x^3-2= (\frac{1}{3})^3-2= \frac{1}{27}-2= \frac{1-54}{27}= -\frac{53}{27}$