The known functions f (x) = loga (x) and G (x) = 2loga (2x + T-2), (a > 0, a ≠ 1, t ∈ R) (1) When t = 4, X ∈ [1,2], and f (x) = g (x) - f (x) has a minimum value of 2, the value of a is obtained (2) When 0 ＜ a ＜ 1, X ∈ [1,2], f (x) ≥ g (x) is constant. Find the value range of real number t Ask God to answer

The known functions f (x) = loga (x) and G (x) = 2loga (2x + T-2), (a > 0, a ≠ 1, t ∈ R) (1) When t = 4, X ∈ [1,2], and f (x) = g (x) - f (x) has a minimum value of 2, the value of a is obtained (2) When 0 ＜ a ＜ 1, X ∈ [1,2], f (x) ≥ g (x) is constant. Find the value range of real number t Ask God to answer

(1)2x+t-2=2x+2
F(x)=2loga(2x+2)-loga(x)=loga=loga(4x+8+4/x)
4X + 4 / X ≥ 8 (basic inequality) if and only if x = 1 / x = 1
Because it is a sign function, 4x + 4 / x + 8 increases monotonically on [1,2]
Because x belongs to, x = 1 has a minimum value of 12 (8 + 8 = 16), and x = 2 has a maximum value of 18
Let s = 4x + 4 / x + 8,
When a > 1, Logas increases monotonically on [1,2], and s increases monotonically, so f (x) increases monotonically. When x = 1, f (1) = loga16 = 2, a = 4 is the minimum value of F (x)
When 0 ＜ a ＜ 1, Logas decreases monotonically on [1,2], s increases monotonically, so f (x) decreases monotonically. When x = 2, f (2) = loga18 = 2, a = 3 Γ 2 ＞ 1 is the minimum of F (x)
So a = 4
Too long did not do the second question, some will not, sorry, can only give you the first question, the process may be some complex, you can have a choice to see
Are you a junior high school student? This seems to be the topic of high school
Γ is the root,

Given the function f (x) = loga (x + 1), G (x) = 2loga (2x + T), if a belongs to (0,1), and X belongs to [0,1], the inequality f (x) > = g (x) holds, and the value range of real number t is obtained

Given the function f (x) = Log &; a &; (x + 1), G (x) = 2log &; a &; (2x + T) (t ∈ R), where x ∈ [0,15]. A ＞ 0, a ≠ 1. (1) if 1 is a solution of the equation f (x) = g (x) about X, find the value of T. (2) when 0 ＜ a ＜ 1, the inequality f (x) ≥ g (x) holds, find the value of T

Calculate (1) (x + 2y-3) (x-2y + 3); & nbsp; & nbsp; (2) (2x3y) 2 · (- 2XY) + (- 2x3y) 3 ÷ (2x2)

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