Let the whole function be f (x) = 2 x+λ * 2 x.
(1) λ=- 1 is substituted into f(x), and f(x)=0, so all zeros are real numbers;
(2) If f (x) is an even function, then f(x)=f(-x), and (1+λ) * 2x = (1+λ) * 2 (-x), and λ =-1;
(3) According to the meaning of the question, 1/2 ≤ (1+λ) * 2 x ≤ 4, and according to the value range of x, the solution is-1-log2 (1+λ) ≥ 0,2-log2 (6544).