Question

Помогите решить неравенства логарифмов!

Answer 1

Ответ:

Объяснение:

a)

$\displaystyle\bf\\log_7(2-x)\leq log_7(3x+6)\\\\\left \{ {{2-x>0} \atop {3x+6>0}} \right. ;\left \{ {{x<2} \atop {x>-2}} \right. ;~~~~-2<x<2\\\\\\7>1\\\\\left \{ {{2-x\leq 3x+6} \atop {x\in(-2;2)}} \right. ;\left \{ {{4x\geq -4} \atop {x\in(-2;2)}} \right. ;\left \{ {{x\geq -1} \atop {x\in(-2;2)}} \right. \\\\\\Otvet:x\in[-1;2)$

б)

$\displaystyle\bf\\log_\frac{1}{4} (2x-5)>-1\\\\\left \{ {{2x-5>0} \atop {log_\frac{1}{4} (2x-5)>log_\frac{1}{4} 4}} \right. \\\\0<\frac{1}{4} <1\\\\\left \{ {{2x>5} \atop {2x-5<4}} \right. ;\left \{ {{x>2,5} \atop {2x<9}} \right. ;\left \{ {{x>2,5} \atop {x<4,5}} \right.~~~~~~2,5<x<4,5 \\\\Otvet:x\in(2,5;4,5)$