Question

Логарифмы! Очень срочно надо 6.39 и 6.41,нужно решение

Answer 1

$log_{0,1}(x^2-x-2) textgreater log_{0,1}(3-x), \ left{begin{array}{c}x^2-x-2 textgreater 0,\3-x textgreater 0,\x^2-x-2 textless 3-x,end{array}right. left{begin{array}{c}(x+1)(x-2) textgreater 0,\x-3 textless 0,\x^2-5 textless 0,end{array}right. \ left{begin{array}{c}(x+1)(x-2) textgreater 0,\x-3 textless 0,\(x+sqrt{5})(x-sqrt{5}) textless 0,end{array}right. left{begin{array}{c} left [{{x textless -1,} atop {x textgreater 2,}} right.\x textless 3,\-sqrt{5} textless x textless sqrt{5},end{array}right. \ left [ {{-sqrt{5} textless x textless -1},} atop {2 textless x textless sqrt{5};}} right. \ xin(-sqrt{5};-1)cup(2;sqrt{5}).$

$log_{0,1}(4-x) geq log_{0,1}10-log_{0,1}(x-1), \ log_{0,1}(4-x)+log_{0,1}(x-1) geq log_{0,1}10, \ log_{0,1}(4-x)(x-1) geq log_{0,1}10, \ left{begin{array}{c}4-x textgreater 0,\x-1 textgreater 0,\(4-x)(x-1) leq 10;end{array}right. left{begin{array}{c}x-4 textless 0,\x-1 textgreater 0,\x^2-5x+4 geq 10;end{array}right. left{begin{array}{c}x textless 4,\x textgreater 1,\x^2-5x-6 geq 0;end{array}right.$
$left{begin{array}{c}x textless 4,\x textgreater 1,\(x+1)(x-6)geq 0;end{array}right. left{begin{array}{c}1<x<4,\ left [ {{x leq -1,} atop {x geq 6;}} right.end{array}right. \ xinvarnothing.$

Answer 2

Спасибо огромное