Question

$| log_{3}x| \geqslant 1$
Помогите решить ​

Answer 1

$\displaystyle |log_3x|\geq 1$

ООФ: x>0

$\displaystyle \left \{ {{log_3(x)\geq 1} \atop {log_3(x)\geq 0}} \right. \\\\\left \{ {{-log_3(x)\geq 1} \atop {log_3(x)< 0}} \right. \\\\\\\left \{ {{x\geq 3} \atop {x\geq 1}} \right. \\\\\left \{ {{x\leq \dfrac{1}{3} } \atop {x<1}} \right. \\\\x\in\Big[3; +\infty\Big)\\x\in\Big(-\infty; \frac{1}{3}\Big ]\\x>0$

Ответ: $x\in\Big(0; \dfrac{1}{3} \Big]\cup\Big[3; +\infty\Big)$