1) 7^(7-3x) ≤ (7)^2
7 > 1
7 - 3x ≤ 2
-3x ≤ 2 - 7
- 3x ≤ - 5
x ≥ 5/3
x ≥ 1(2/3)
x ∈[1(2/3) ; + ≈)
2) 3^(2x-1) + 3^(2x-2) - 3^(2x-4) = 315
(3^2x)* (1/3 + 1/9 - 1/81) = 315
(3^2x)/(35/81) = 315
(3^2x) = 81*9
(3^2x) (3^6)
2x = 6
x = 3
3) 5^(3x-7) = 8^[(3x-7)/3]
5^(3x-7) = 2^(3x-7)
(5/2)^(3x-7) = 1
(5/2)^(3x-7) = (5/2)^0
3x - 7 = 0
3x = 7
x = 7/3
x = 2(1/3)
4) a) 3*(3^2x) - 10*(3^x) + 3 < 0
3^x = z
z^2 - 10z + 3 = 0
D = 100 - 4*3*3 = 64
1) z = (10 - 8)/6
z1 = 1/3
3^x = 3^(-1)
x1 = - 1
z = (10 + 8)/6
z2 = 3
3^x = 3
x2 = 1
+ - +
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-1 1 x
x ∈(-1;1)
b) 4 + 2/(3^x - 1) = 5/(3^(x-1)
4*(3^x - 1) + 2 = [15*(3^x - 1)] / (3^x)
4*(3^x -1) + 2 = 15 - 15/(3^x)
4*(3^x) - 17 - 15*(3^x) = 0
4*(3^2x) - 17*(3^x) - 15 = 0
3^x = z> 0
4*(z^2) - 17z - 15 = 0
D = 289 + 4*4*15 = 529
z1 = (17 - 23)/8
z1 = -6/8
z1 = - 2/3 < 0 посторонний корень
z2 = (17+23)/8
z2 = 40/8
z2 = 5
3^x = 5
x = log_3 (5)