209 1) 27x = 1/3; 2) 400x = 1/20; 3) (1/5)x = 25; 4) (3/1)x = 1/81

1. $$27^x = \frac{1}{3}$$

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

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

   $$3x = -1$$

   $$x = -\frac{1}{3}$$

2. $$400^x = \frac{1}{20}$$

   $$20^{2x} = 20^{-1}$$

   $$2x = -1$$

   $$x = -\frac{1}{2}$$

3. $$(\frac{1}{5})^x = 25$$

   $$5^{-x} = 5^{2}$$

   $$x = -2$$

4. $$(\frac{3}{1})^x = \frac{1}{81}$$

   $$3^x = 3^{-4}$$

   $$x = -4$$

Ответ: -1/3; -1/2; -2; -4