Verified answer

2^x-1 + 2^x + 2^x+1 - 2^x+2 + 2^x+3=120

2^x*(1/2 + 1 + 2 - 4 + 8) = 120

2^x*(1 + 2 + 4 - 8 + 16) = 240

2^x*15 = 240

2^x = 240/15 = 16

x = 4

pronto

Suponho a interpretação assim;

(2^X)/2 + 2^X + 2(2^X) + 4(2^X) + 8(2^X) = 120

(2^X)(1/2 + 1 + 2 + 4 +8)= 120

(2^X)(31/2) = 120

2^(X-1) = (120/31)

(X-1) = LOG(base 2)de (120/31)

X = 1 + LOG(2)(120/31)