2 exponent x=144 base x find x,the answer is 6,but i cant figure out the workings

Answer 1

You want a power of two to be

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

So, which powers of 2 are perfect squares? There are lots of answers:

(6+2)^2 = 64 = 6^2 + 4*6 + 4 = 144₆ = 2^6

(14+2)^2 = 256 = 144₁₄ = 2^8

All even powers of 2 are perfect squares.