Question

Алгебра. 11 класс. Помогите, пожалуйста ​

Answer 1

Ответ:

Объяснение:

$\displaystyle\\a)~\log_\frac{1}{2} (2x-4)\geq \log_\frac{1}{2} (x+1)\\\\0<\frac{1}{2} <1\\\\\left \{ {\bigg{2x-4>0} \atop\big {x+1>0}}\atop \bigg{2x-4\leq x+1}} \right. \Leftrightarrow\left \{ {{x>2} \atop {x\leq 5}} \right. \\\\\\Otvet:x\in(2;5]$

-------------------------------------------------------------------------

$\displaystyle\\b)~\log_2(x-3)+\log_3(x-2)\leq 1\\\\\log_2(x-3)(x-2)\leq \log_22\\\\2>1\\\\\left \{ {\bigg{x-3>0} \atop\big {x-2>0}}\atop \big{(x-3)(x-2)\leq 2} \right. \Leftrightarrow\left \{ {{x>3} \atop {x^2-3x-2x+6-2\leq0}} \right. \\\\\\\left \{ {{x>3} \atop {x^2-5x+4\leq 0}} \right. \Leftrightarrow\left \{ {{x>3} \atop {(x-1)(x-4)\leq 0}} \right. \Leftrightarrow\left \{ {{x>3} \atop {1\leq x\leq 4 }} \right. \\\\\\Otvet:x\in(3;4]$