Решение
1) 4^(x² + 7x + 9) = 4⁻¹
x² + 7x + 9 = - 1
x² + 7x + 10 = 0
x₁ = - 2
x₂= - 5
2) 6^(2x) - 35*(6^x) - 36 = 0
6^x = t, t > 0
t² - 35t - 36 = 0
t₁ = - 1, не удовлетворяет условию t > 0
t₂ = 36
6^x = 36
6^x = 6²
x = 2
3) 5^(x - 1) - 3*5^(x + 1) = - 370
(1/5)*5^x - 3*5*5^x = - 370
(5^x)*(1/5 - 15) = - 370
(5^x)*(- 74/5) = - 370
5^x = (- 370) : (- 74/5)
5^x = 25
5^x = 5²
x = 2