Question

Решите неравенство:
(4x-1)log₂x≥0

Answer 1

$(4x-1)\log_2x \geq 0 \\ \\ \left\{\begin{matrix} \left \{ {{4x-1 \geq 0} \atop {x\ \ \textless \ \ 0}} \right.\\ \log_2 x\geq 0 \end{matrix}\right.\to \left\{\begin{matrix} \left \{ {{4x \geq 1} \atop {x\ \textless \ 0}} \right. \\ \log_2x \geq \log_21 \end{matrix}\right.\to \left\{\begin{matrix} \left \{ {{x \geq \frac{1}{4} } \atop {x\ \textless \ 0}} \right.\\ x \geq 1 \end{matrix}\right.$

Ответ: $x \in (0; \frac{1}{4} ]\cup [1;+\infty)$