1. Solve the inequality

$$
\frac{9^{x}-5 \cdot 15^{x}+4 \cdot 25^{x}}{-9^{x}+8 \cdot 15^{x}-15 \cdot 25^{x}}<0
$$
Solution. We will write the inequality in the form

$$
\frac{\left(\frac{3}{5}\right)^{2 x}-5 \cdot\left(\frac{3}{5}\right)^{x}+4}{-\left(\frac{3}{5}\right)^{2 x}+8 \cdot\left(\frac{3}{5}\right)^{x}-15}0
$$

The solution to the last inequality is the set $(0,1) \cup(3,4) \cup(5, \infty)$. According to this, the solution to the original inequality is the set

$$
x \in\left(-\infty, \log _{\frac{3}{5}} 5\right) \cup\left(\log _{\frac{3}{5}} 4, \log _{\frac{3}{5}} 3\right) \cup(0, \infty)
$$