If a line y = ex + B (E is the base of natural logarithm) and two functions f (x) = ex, G (x) = LNX have at most one common point, then the value range of real number B is______ ．

If a line y = ex + B (E is the base of natural logarithm) and two functions f (x) = ex, G (x) = LNX have at most one common point, then the value range of real number B is______ ．

When y = ex + B and f (x) = ex have a common point, it is transformed into that ex + B = ex has only one root, Let f (x) = ex - (ex + b), then its derivative function is f / (x) = ex-e, so when f / (x) > 0, x > 1, and F / (x) < 0, x < 1, then f (x) takes the minimum value f (1) = - B when x = 1, so when y = ex + B and f (x) = ex have a common point, then - B = 0, that is b = 0 ）If there is no common point, it must be - B ＞ 0, that is, B ＜ 0. Similarly, when y = ex + B and G (x) = LNX have a common point, B = - 2, when y = ex + B and G (x) = LNX have no common point, B ＞ - 2 When B = - 2, there is no common point with the image of the two functions, - 2 ＜ B ＜ 0. To sum up, we can know [- 2, 0], so the answer is: [- 2, 0]