Вариант 2 1. log₆ (3 - x) = 2; log₃ (9 + x) = 4; log₃ (14-x) = log₃ 5; 2. log₁₁ (16 + x) = log₁₁ 12; log₈(13-x) = -2; log₂(4 - x) = 2 log₂ 5; 3. log₉ (x + 6) = log₉ (4x - 9); log₃ (x² + 4x) = log₃(x² + 4).

Решим каждое уравнение.

1. log₆ (3 - x) = 2

   3 - x = 6²

   3 - x = 36

   -x = 33

   x = -33

   Проверим:

   log₆ (3 - (-33)) = log₆ (36) = 2. Верно.

   log₃ (9 + x) = 4

   9 + x = 3⁴

   9 + x = 81

   x = 72

   Проверим:

   log₃ (9 + 72) = log₃ (81) = 4. Верно.

   log₃ (14-x) = log₃ 5

   14 - x = 5

   -x = -9

   x = 9

   Проверим:

   log₃ (14 - 9) = log₃ (5). Верно.

2. log₁₁ (16 + x) = log₁₁ 12

   16 + x = 12

   x = -4

   Проверим:

   log₁₁ (16 + (-4)) = log₁₁ (12). Верно.

   log₈(13-x) = -2

   13 - x = 8⁻²

   13 - x = 1/64

   x = 13 - 1/64

   x = (13 * 64 - 1)/64

   x = 831/64

   Проверим:

   log₈(13 - 831/64) = log₈((832 - 831)/64) = log₈(1/64) = -2. Верно.

   log₂(4 - x) = 2 log₂ 5

   log₂(4 - x) = log₂ 5²

   4 - x = 25

   -x = 21

   x = -21

   Проверим:

   log₂(4 - (-21)) = log₂(25) = log₂ 5². Верно.

3. log₉ (x + 6) = log₉ (4x - 9)

   x + 6 = 4x - 9

   -3x = -15

   x = 5

   Проверим:

   log₉ (5 + 6) = log₉ (4*5 - 9)

   log₉ (11) = log₉ (11). Верно.

   log₃ (x² + 4x) = log₃(x² + 4)

   x² + 4x = x² + 4

   4x = 4

   x = 1

   Проверим:

   log₃ (1² + 4*1) = log₃(1² + 4)

   log₃ (5) = log₃ (5). Верно.

Ответ: Решения уравнений найдены выше.