Логарифмы (задание во вложении)

$5^{\sin \pi x} + \frac{5}{5^{\sin \pi x}} \geq 6 \\ \\ t=5^{\sin \pi x} \ (t\ \textgreater \ 0) \\ \\ t+\frac{5}{t}-6 \geq 0; \ \ \ \ t+\frac{5}{t}-6=0 \\ \\ t^2 -6t+5=0; \ \ t_{1,2}=\frac{6 \pm \sqrt{36 - 20}}{2}=\frac{6 \pm 4}{2} \\ \\ t_1=5; \ \ t_2=1$

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$t \leq 1\ \cup \ t \geq 5 \\ \\ 5^{\sin \pi x} \leq 1 \ \cup \ 5^{\sin{\pi x}} \geq 5 \\ \\ \sin \pi x \leq0 \ \cup \ \sin{\pi x} \geq 1 \\ \\ -\pi + 2\pi n \leq \pi x \leq 2\pi n \ \cup \ \sin{\pi x} = 1 \\ \\ -1+ 2 n \leq x \leq 2 n \ \cup \ \pi x = \frac{\pi}{2}+ 2 \pi n, \ n \in Z \\ \\ 2 n-1 \leq x \leq 2 n \ \cup \ x = \frac{1}{2}+ 2 n, \ n \in Z$