Question

2^x-3 +2^x-4= 2^x-2 - 2^x-1 + 14

Answer 1

2^x = y

2^x*2^(-3) + 2^x*2^(-4) = 2^x*2^(-2) - 2^x*2^(-1) + 14
y*1/8 + y*1/16 = y*1/4 - y*1/2 + 14

(2y+y) / 16 = (y-2y+56) / 4

3y / 4 = -y+56

3y = -4y+224

3y+4y = 224

7y = 224

y = 224/7

y = 32

Voltando:

2^x = 32

2^x = 2^5

Como as bases são iguais, o valor de x é:

x = 5