Given the inequality:
$$\frac{\log{\left(9 x \right)} \log{\left(64 x \right)}}{\left(5 x^{2} - \left|{x}\right|\right) \log{\left(3 \right)} \log{\left(4 \right)}} \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\log{\left(9 x \right)} \log{\left(64 x \right)}}{\left(5 x^{2} - \left|{x}\right|\right) \log{\left(3 \right)} \log{\left(4 \right)}} = 0$$
Solve:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
$$x_0 = 0$$
$$\frac{\log{\left(9 \cdot 0 \right)} \log{\left(64 \cdot 0 \right)}}{\left(5 \cdot 0^{2} - \left|{0}\right|\right) \log{\left(3 \right)} \log{\left(4 \right)}} \leq 0$$
zoo <= 0
so the inequality is always executed