212 1) 5x = 8x; 2) (1/2)x = (2/3)x; 3) 3x = 52x; 4) 4x = 32/x

1. $$5^x = 8^x$$

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

   $$x = 0$$

2. $$(\frac{1}{2})^x = (\frac{2}{3})^x$$

   $$(\frac{1}{2} \cdot \frac{3}{2})^x = 1$$

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

   $$x = 0$$

3. $$3^x = 5^{2x}$$

   $$3^x = 25^x$$

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

   $$x = 0$$

4. $$4^x = 32^{\frac{x}{x}}$$

   $$4^x = 32^1$$

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

   $$2x = 5$$

   $$x = 2,5$$

Ответ: 0; 0; 0; 2,5