Задание 11. Найдите корень уравнения: 1) 22x-1.2-4x-3=16 2) 94x+1.93-2x = 81 3) 115x+1.113-x=121 4) 62x-6.6-3x+5 = 216 5) 6-5x-2:63x+4 = 36 6) 42x+3:4-6x+4 = 64 7) 36x+5:33x-2=81 8) 132x+3:13-4x-11 =169 Задание 12. Найдите корень уравнения: x-8 1 1 = - 5 25 x+9 1 2 = 64

Ответ: Решения заданий 11 и 12 представлены ниже.

Задание 11

1. 2^2x-1 ⋅ 2^-4x-3 = 16

   2^2x-1-4x-3 = 2⁴

   2x - 1 - 4x - 3 = 4

   -2x - 4 = 4

   -2x = 8

   x = -4

2. 9^4x+1 ⋅ 9^3-2x = 81

   9^4x+1+3-2x = 9²

   4x + 1 + 3 - 2x = 2

   2x + 4 = 2

   2x = -2

   x = -1

3. 11^5x+1 ⋅ 11^3-x = 121

   11^5x+1+3-x = 11²

   5x + 1 + 3 - x = 2

   4x + 4 = 2

   4x = -2

   x = -0.5

4. 6^2x-6 ⋅ 6^-3x+5 = 216

   6^2x-6-3x+5 = 6³

   2x - 6 - 3x + 5 = 3

   -x - 1 = 3

   -x = 4

   x = -4

5. 6^-5x-2 : 6^3x+4 = 36

   6^-5x-2-3x-4 = 6²

   -5x - 2 - 3x - 4 = 2

   -8x - 6 = 2

   -8x = 8

   x = -1

6. 4^2x+3 : 4^-6x+4 = 64

   4^2x+3+6x-4 = 4³

   2x + 3 + 6x - 4 = 3

   8x - 1 = 3

   8x = 4

   x = 0.5

7. 3^6x+5 : 3^3x-2 = 81

   3^6x+5-3x+2 = 3⁴

   6x + 5 - 3x + 2 = 4

   3x + 7 = 4

   3x = -3

   x = -1

8. 13^2x+3 : 13^-4x-11 = 169

   13^2x+3+4x+11 = 13²

   2x + 3 + 4x + 11 = 2

   6x + 14 = 2

   6x = -12

   x = -2

Задание 12

1. (\( \frac{1}{5} \))^x-8 = \( \frac{1}{25} \)

   (\( \frac{1}{5} \))^x-8 = (\( \frac{1}{5} \))²

   x - 8 = 2

   x = 10

2. (\( \frac{1}{4} \))^x+9 = \( \frac{1}{64} \)

   (\( \frac{1}{4} \))^x+9 = (\( \frac{1}{4} \))³

   x + 9 = 3

   x = -6

Ответ: Решения заданий 11 и 12 представлены выше.