5. Solve the inequality $\left(3^{x^{2}-1}-9 \cdot 3^{5 x+3}\right) \log _{\cos \pi}\left(x^{2}-6 x+9\right) \geq 0$.

#
# Solution:

Domain: $(x-3)^{2}>0, \quad \cos \pi x>0, \cos \pi x \neq 1, \Rightarrow x \in(-0.5+2k ; 2k) \cup(2k ; 0.5+2k), k \in Z$.

The original inequality on the domain is equivalent to the following

$$
\left(x^{2}-5 x-6\right)(\cos \pi x-1)\left(x^{2}-6 x+8\right) \geq 0 \Leftrightarrow(x-6)(x+1)(x-2)(x-4) \leq 0 \Rightarrow
$$

$x \in[-1 ; 2] \cup[4 ; 6]$.

Considering the domain, we have $\quad x \in(-0.5 ; 0) \cup(0 ; 0.5) \cup(1.5 ; 2) \cup(4 ; 4.5) \cup(5.5 ; 6)$.

Answer: $x \in(-0.5 ; 0) \cup(0 ; 0.5) \cup(1.5 ; 2) \cup(4 ; 4.5) \cup(5.5 ; 6)$.