210 1) 3x+1 = 9; 2) 2 . 4x = 64; 3) 3x+2 . 3x-2 = 1; 4) 0,5x+7 . 0,51-2x = 2; 5) 0,6x . 0,63 = 0,62x/0,65; 6) 63x . 1/6 = 6/62x

1. $$3^{x+1} = 9$$

   $$3^{x+1} = 3^2$$

   $$x+1 = 2$$

   $$x = 1$$

2. $$2 \cdot 4^x = 64$$

   $$2 \cdot (2^2)^x = 2^6$$

   $$2^{2x+1} = 2^6$$

   $$2x + 1 = 6$$

   $$2x = 5$$

   $$x = 2,5$$

3. $$3^{x+2} \cdot 3^{x-2} = 1$$

   $$3^{(x+2) + (x-2)} = 1$$

   $$3^{2x} = 1$$

   $$2x = 0$$

   $$x = 0$$

4. $$0,5^{x+7} \cdot 0,5^{1-2x} = 2$$

   $$0,5^{(x+7) + (1 - 2x)} = 2$$

   $$0,5^{8 - x} = 2$$

   $$0,5^{8 - x} = 0,5^{-1}$$

   $$8 - x = -1$$

   $$x = 9$$

5. $$0,6^x \cdot 0,6^3 = \frac{0,6^{2x}}{0,6^5}$$

   $$0,6^{x+3} = 0,6^{2x-5}$$

   $$x + 3 = 2x - 5$$

   $$x = 8$$

6. $$6^{3x} \cdot \frac{1}{6} = \frac{6}{6^{2x}}$$

   $$6^{3x-1} = 6^{1-2x}$$

   $$3x - 1 = 1 - 2x$$

   $$5x = 2$$

   $$x = 0,4$$

Ответ: 1; 2,5; 0; 9; 8; 0,4