If the equation a2x + (1 + LGM) ax + 1 = 0 (a > 0 and a ≠ 1) of X has a solution, then the value range of M is______ ．

If the equation a2x + (1 + LGM) ax + 1 = 0 (a > 0 and a ≠ 1) of X has a solution, then the value range of M is______ ．

Let t = ax (T > 0), then the equation is transformed into T2 + (1 + LGM) t + 1 = 0 and has a solution on (0, + ∞). So △ = (1 + LGM) 2 − 4 ≥ 0t = − 1 + lgm2 > 0, the solution is LGM ≤ - 3, so 0 < m ≤ 10-3, so the answer is: (0, 10-3]

Let a > 0, tangent A is not equal to 1, if the maximum value of function y = a ^ (2x) + 2 (a ^ x) - 1 on [- 1,1] is 14, find the value of A

Let t = a ^ x, then t > 0 and t ≠ 1
y=t²+2t-1=(t+1)²-2
When 0