Question

log₄(2х-7)≤2 решите логарифмические неравенство

Answer 1

Ответ:

$\left \{ {{ x \leq 11,5} \atop {x > 3,5}} \righ$ или (3,5; 11,5]

Пошаговое объяснение:

ОДЗ: $2x - 7 > 0$

Решаем неравенство:

$\left \{ {{ log_4(2x - 7) \leq 2} \atop {2x - 7 > 0}} \right. \\\\\left \{ {{ log_4(2x - 7) \leq log_4 4^2} \atop {2x > 7 }} \right.\\\\\left \{ {{ 2x - 7\leq 4^2} \atop {x > 7 : 2}} \right\\\\\left \{ {{ 2x - 7\leq 16} \atop {x > 3,5}} \right\\\\\left \{ {{ 2x \leq 16 + 7} \atop {x > 3,5}} \right\\\\\left \{ {{ 2x \leq 23} \atop {x > 3,5}} \right\\\\\left \{ {{ x \leq 23 : 2} \atop {x > 3,5}} \right\\\\\left \{ {{ x \leq 11,5} \atop {x > 3,5}} \right$