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Получилось, но не уверен, что все правильно
Самое главное - свести части к одинаковым основаниям.
6) a) (3/2)^x = (4/9)^4 = ((2/3)^2)^4
(3/2)^x = (2/3)^8 = (3/2)^(-8)
x = -8
б) 12^(x+1) = 15
x + 1 =
x =
в) (2/5)^(x-1)*(25/8)^(x-1) = 125/64
2^(x-1)/5^(x-1)*5^(2x-2)/2^(3x-3) = 5^3/4^3
2^(x-1)/2^(3x-3) * 5^(2x-2)/5^(x-1) = 5^3/4^3
1/2^(2x-2)*5^(x-1) = 5^(x-1)/4^(x-1) = 5^3/4^3
x - 1 = 3
x = 4
7) a) (1/2)^(x^2-1) = 1/8*(1/32)^(x^2-1)
(1/2)^(x^2-1)*32^(x^2-1) = 1/8
(32/2)^(x^2-1) = 16^(x^2-1) = 1/8
2^(4x^2-4) = 2^(-3)
4x^2-4 = -3
x^2 = 1/4
x1 = -1/2; x2 = 1/2
б) (0,5)^(x^2)*(1/2)^x = 1/4
(1/2)^(x^2+x) = (1/2)^2
x^2 + x = 2
x^2 + x - 2 = 0
x1 = 1; x2 = -2
в)![\sqrt[3]{4^{x+1}} *16 = \sqrt{4^{x^2}}](https://tex.z-dn.net/?f=+%5Csqrt%5B3%5D%7B4%5E%7Bx%2B1%7D%7D+%2A16+%3D++%5Csqrt%7B4%5E%7Bx%5E2%7D%7D+)
(x+1)/3 + 2 = x^2/2
Умножаем все на 6
2(x + 1) + 12 = 3x^2
3x^2 - 2x - 14 = 0
D = 4 + 4*3*14 = 172 = 4*43
x1 = (2 - 2V(43))/6 = (1 - V(43))/3
x2 = (2 + 2V(43))/6 = (1 + V(43))/3
Вот за эти иррациональности я не уверен.
Самое главное - свести части к одинаковым основаниям.
6) a) (3/2)^x = (4/9)^4 = ((2/3)^2)^4
(3/2)^x = (2/3)^8 = (3/2)^(-8)
x = -8
б) 12^(x+1) = 15
x + 1 =
x =
в) (2/5)^(x-1)*(25/8)^(x-1) = 125/64
2^(x-1)/5^(x-1)*5^(2x-2)/2^(3x-3) = 5^3/4^3
2^(x-1)/2^(3x-3) * 5^(2x-2)/5^(x-1) = 5^3/4^3
1/2^(2x-2)*5^(x-1) = 5^(x-1)/4^(x-1) = 5^3/4^3
x - 1 = 3
x = 4
7) a) (1/2)^(x^2-1) = 1/8*(1/32)^(x^2-1)
(1/2)^(x^2-1)*32^(x^2-1) = 1/8
(32/2)^(x^2-1) = 16^(x^2-1) = 1/8
2^(4x^2-4) = 2^(-3)
4x^2-4 = -3
x^2 = 1/4
x1 = -1/2; x2 = 1/2
б) (0,5)^(x^2)*(1/2)^x = 1/4
(1/2)^(x^2+x) = (1/2)^2
x^2 + x = 2
x^2 + x - 2 = 0
x1 = 1; x2 = -2
в)
(x+1)/3 + 2 = x^2/2
Умножаем все на 6
2(x + 1) + 12 = 3x^2
3x^2 - 2x - 14 = 0
D = 4 + 4*3*14 = 172 = 4*43
x1 = (2 - 2V(43))/6 = (1 - V(43))/3
x2 = (2 + 2V(43))/6 = (1 + V(43))/3
Вот за эти иррациональности я не уверен.
