Given that the definition and range of exponential function f (x) = a ^ X are (m.n), the value range of a is obtained

Given that the definition and range of exponential function f (x) = a ^ X are (m.n), the value range of a is obtained

a> When y = a ^ x is tangent to y = x, the tangent point (x0, Y0) is considered
Dy / DX = LNA. A ^ x = 1, and a ^ x0 = x0, LNA = 1 / x0, a = e ^ (1 / x0)
A ^ x0 = x0, a = x0 ^ (1 / x0), that is, e ^ (1 / x0) = x0 ^ (1 / x0),
X0 > 1, x ^ (1 / x0) is a monotone function when x > 0, and x0 = e is obtained
A = e ^ (1 / E)
When 1