211 1) 3²ˣ⁻¹ + 3²ˣ = 108; 2) 2³ˣ⁺² − 2³ˣ⁻² = 30; 3) 2ˣ⁺¹ + 2ˣ⁻¹ + 2ˣ = 28; 4) 3ˣ⁻¹ − 3ˣ + 3ˣ⁺¹ = 63.

1) 3^2x-1 + 3^2x = 108

3^2x / 3 + 3^2x = 108

3^2x * (1/3 + 1) = 108

3^2x * (4/3) = 108

3^2x = 108 * (3/4)

3^2x = 27 * 3

3^2x = 3³ * 3¹

3^2x = 3⁴

2x = 4

x = 2

2) 2^3x+2 - 2^3x-2 = 30

2^3x * 2² - 2^3x / 2² = 30

2^3x * (4 - 1/4) = 30

2^3x * (15/4) = 30

2^3x = 30 * (4/15)

2^3x = 2 * 4

2^3x = 2³

3x = 3

x = 1

3) 2^x+1 + 2^x-1 + 2^x = 28

2^x * 2 + 2^x / 2 + 2^x = 28

2^x * (2 + 1/2 + 1) = 28

2^x * (7/2) = 28

2^x = 28 * (2/7)

2^x = 4 * 2

2^x = 2³

x = 3

4) 3^x-1 - 3^x + 3^x+1 = 63

3^x / 3 - 3^x + 3^x * 3 = 63

3^x * (1/3 - 1 + 3) = 63

3^x * (7/3) = 63

3^x = 63 * (3/7)

3^x = 9 * 3

3^x = 3² * 3¹

3^x = 3³

x = 3

Ответ: 1) x = 2; 2) x = 1; 3) x = 3; 4) x = 3