Question

determine o valor x para que se tenha 2ˣ⁻¹ + 2ˣ⁺³ + 2ˣ⁻² + 2ˣ = 2496

Answer 1

2^x - 1 + 2^x + 3  + 2^x - 2 + 2^x = 2496
2^x . 2^-1 + 2 ^x . 2^3 + 2 ^x . 2^-2 + 2^x = 2496
2^x . (1/2)^1 + 2^x . 8 + 2^x . (1/2)^2 + 2^x = 2496
2^x = y
y.(1/2) + y. 8  + y . 1/4 + y = 2496
1/2.y + 8 y + (1/4)y  + y = 2496
m.m.c = 4
(2/4).y + (32/4).y + (1/4).y + (4/4).y = 9984/4  (eliminando o denominador)
2 y + 32 y + 1 y + 4 y = 9984
 39.y = 9984
y = 9984 / 39
y = 256
2^x = y
2^x = 256
2^x = 2^8
x = 8

Answer 2

Boa noite

2^(x - 1) + 2^(x + 3) + 2^(x - 2) + 2^x = 2496 

2^x * (1/2 + 8 + 1/4 + 1) = 2496 =)
2^x * (2 + 32 + 1 + 4) = 4*2496 
2^x * 39 = 4*2496 
2^x =  4*2496 /39 = 256

2^x = 2^8
x = 8