Решите неравенство: [latex]log_{3x - 1}16 extless 2[/latex]
Решите неравенство: [latex]log_{3x - 1}16 extless 2[/latex]
Answers
ОДЗ {3x-1>0⇒x>1/3 {3x-1≠1⇒x≠2/3 x∈(1/3;2/3) U (2/3;∞) 1)x∈(1/3;2/3) (3x-1)²<16 (3x-1)²-16<0 (3x-1-4)(3x-1+4)<0 (3x-5)(3x+3)<0 x=5/3 x=-1 \\\\\ \\\\\\\\\\\\\\\\\ + _ + -------(-1)------(1/3)---------(2/3)----(5/3)---------------- \\\\\\\\\\ x∈(1/3;2/3) 2)x∈(2/3;∞) (3x-1)²>16 (3x-5)(3x+3)>0 \\\\\ \\\\\\\\\\\\\\\\\ + _ + -------(-1)------(1/3)---------(2/3)----(5/3)---------------- /////////////////////////// x∈(5/3;∞) Ответ x∈(1/3;2/3) U (5/3;∞)
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