Question

Решите логарифмическое неравенство (2x-3) log2 x>=0

Answer 1

$(2x-3)\cdot log_2x\geq 0\; \; ,\quad ODZ:\; \; x>0\\\\a)\; \; \left \{ {{2x-3\geq 0} \atop {log_2x\geq 0}} \right. \; \left \{ {{x\geq 1,5} \atop {x\geq 1\; ,\; x>0}} \right. \; \; \Rightarrow \; \; x\geq 1,5\\\\b)\; \; \left \{ {{2x-3\leq 0} \atop {log_2x\leq 0}} \right. \; \left \{ {{x\leq 1,5} \atop {x\leq 1\; ,\; x>0}} \right. \; \; \Rightarrow \; \; 0<x\leq 1\\\\Otvet:\; \; x\in (0;1\, ]\cup [\, 1,5\, ;\, +\infty )$

Answer 2

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