Решение
3.
a) 5^(x + 1) - 5^x - 100 = 0
5*(5^x) - 5^x = 100
(5^x)*(5 - 1) = 100
5^x = 100/4
5^x = 25
5^x = 5²
x = 2
б) 3*(9^2x) - 10*(9^x) + 3 = 0
9^x = t, t > 0
3t² - 10t + 3 = 0
D = 100 - 4*3*3 = 64
t₁ = (10 - 8)/6
t₁ = 1/3
t₂ = (10 + 8)/6
t₂ = 3
1) 9^x = 1/3
3^2x = 3⁻¹
2x = - 1
x₁ = -1/2
2) 9^x = 3
3^2x = 3¹
2x = 1
x₂ = 1/2
4.
16^(x - 0,5) - 5*4^(x - 1) + 2 = 0
(4^2x)*(1/4) - 5*(4^x)*(1/4) + 2 = 0 умножаем на 4
4^(2x) - 5*(4^x) + 8 = 0
4^x = t
t² - 5t + 8 = 0
D = 25 - 4*1*8 = - 7 < 0 решений нет