8) + = 150

8) $$\left( \frac{1}{5} \right)^{2x-1} + \left( \frac{1}{5} \right)^{2x} = 150$$

$$\frac{\left( \frac{1}{5} \right)^{2x}}{\frac{1}{5}} + \left( \frac{1}{5} \right)^{2x} = 150$$

$$5 \cdot \left( \frac{1}{5} \right)^{2x} + \left( \frac{1}{5} \right)^{2x} = 150$$

$$6 \cdot \left( \frac{1}{5} \right)^{2x} = 150$$

$$\left( \frac{1}{5} \right)^{2x} = 25$$

$$\left( \frac{1}{5} \right)^{2x} = \left( \frac{1}{5} \right)^{-2}$$

$$2x = -2$$

$$x = -1$$

Ответ: -1