Решение уравнений:

1) (25/9) ^x * (27/125) ^x-5 = 5/3

2) (5/6) ^x^2-2x = (5/6) ^6-x

3) 2^1-x^2*2^2x=64^-1

1. (25/9) ^x * (27/125) ^ (x-5) = 5/3, ((5/3) ²) ^x * ((3/5) ³) ^ (x-5) = 5/3

(5/3) ^ (2x) * (3/5) ^ (3x-15) = 5/3, (5/3) ^ (2x) * ((5/3) ⁻¹) ^ (3x-15) = 5/3

((5/3) ^ (2x)) * ((5/3) ^ (-3x+15)) = 5/3, ((5/3) ^ (2x-3x)) * ((5/3) ¹⁵) = 5/3

(5/3) ^ (-x) = (5/3) : (5/3) ¹⁵, (5/3) ^ (-x) = (5/3) ⁻¹⁴

-x=-14, x=14

2. (5/6) ^ (x²-2x) = (5/6) ^ (6-x)

x²-2x=6-x, x²-x-6=0, x₁=3, x₂=-2

3. 2^ (1-x) * 2^ (2x) = 64⁻¹

2^ (1-x+2x) = (2⁶) ⁻¹

2^ (1+x) = 2⁻⁶

1+x=-6, x=-7