Given that x=1, find the values for a and b that make the equation true: (2^a)^4x = (2^b)^x+1

Answer 1

(2^a)^4x = (2^b)^{x + 1}

Substitute x = 1 in this equation:

(2^a)^4•1 = (2^b)¹⁺¹

(2^a)⁴ = (2^b)²

(2)^4a = (2)^2b

4a = 2b

b = 2a

Possible pairs (a, b): 1, 2; 2, 4; 3, 6; etc.