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

Решим уравнения:

1. $$2^{2x-1} \cdot 2^{-4x-3} = 16$$
   $$2^{2x-1-4x-3} = 2^4$$
   $$2^{-2x-4} = 2^4$$
   $$-2x-4 = 4$$
   $$-2x = 8$$
   $$x = -4$$
2. $$9^{4x+1} \cdot 9^{3-2x} = 81$$
   $$9^{4x+1+3-2x} = 9^2$$
   $$9^{2x+4} = 9^2$$
   $$2x+4 = 2$$
   $$2x = -2$$
   $$x = -1$$
3. $$11^{5x+1} \cdot 11^{3-x} = 121$$
   $$11^{5x+1+3-x} = 11^2$$
   $$11^{4x+4} = 11^2$$
   $$4x+4 = 2$$
   $$4x = -2$$
   $$x = -\frac{1}{2} = -0.5$$
4. $$6^{2x-6} \cdot 6^{-3x+5} = 216$$
   $$6^{2x-6-3x+5} = 6^3$$
   $$6^{-x-1} = 6^3$$
   $$-x-1 = 3$$
   $$-x = 4$$
   $$x = -4$$
5. $$6^{5x-2} : 6^{3x+4} = 36$$
   $$6^{5x-2 - (3x+4)} = 6^2$$
   $$6^{5x-2-3x-4} = 6^2$$
   $$6^{2x-6} = 6^2$$
   $$2x-6 = 2$$
   $$2x = 8$$
   $$x = 4$$
6. $$4^{2x+3} : 4^{-6x+4} = 64$$
   $$4^{2x+3 - (-6x+4)} = 4^3$$
   $$4^{2x+3+6x-4} = 4^3$$
   $$4^{8x-1} = 4^3$$
   $$8x-1 = 3$$
   $$8x = 4$$
   $$x = \frac{1}{2} = 0.5$$
7. $$3^{6x+5} : 3^{3x-2} = 81$$
   $$3^{6x+5 - (3x-2)} = 3^4$$
   $$3^{6x+5-3x+2} = 3^4$$
   $$3^{3x+7} = 3^4$$
   $$3x+7 = 4$$
   $$3x = -3$$
   $$x = -1$$
8. $$13^{2x+3} : 13^{-4x-11} = 169$$
   $$13^{2x+3 - (-4x-11)} = 13^2$$
   $$13^{2x+3+4x+11} = 13^2$$
   $$13^{6x+14} = 13^2$$
   $$6x+14 = 2$$
   $$6x = -12$$
   $$x = -2$$

Ответ: 1) -4; 2) -1; 3) -0.5; 4) -4; 5) 4; 6) 0.5; 7) -1; 8) -2