Assume t =2^x
t^2-2t-3 = 0
(t-3)(t+1) = 0
t = 3, 2^x = 3, Take log on both sides. x = log(3)/log 2
t = -1, 2^x should be alwasy > 0. No solution for x.
Let t =2^x
t^2-2t-3 = 0
(t-3)(t+1) = 0
t = 3, 2^x = 3, Take log on both sides. x = log(3)/log 2
t = -1, it is impossible for 2^x <0. So, no solution for real x.
group like terms ans solve for x
4^x - 2^x=3-1 remember the sign changes when it crosses the equals sign
now 4^x- 2^x= 2^x
and 3-1=2 so the new equation is
2^x=2 solve for x by dividing by both sides by 2
x=1
OK, if the "x + 1" is in the exponent of the second term, then it should be written as 2^(x + 1) to avoid confusion. Hint "write as a quadratic" probably also means you left off the "square" and it should be 4 to the x-square power. Otherwise you have a nonsense equation because 4^x IS 2^(x+1)
and you are trying to "solve" x - x = 3, which is false every time.