values-of-x-satisfy-log_2x2-2x-3-cfwhu","difficulty":"medium","question_text":"Which values of $x$ satisfy $\\log_2(x^2 - 2x) < 3$?","choices":[{"id":"a","text":"$$x \\in (-2, 0) \\cup (2, 4)$"},{"id":"b","text":"$$x \\in (-2, 4)$"},{"id":"c","text":"$$x \\in (0, 2)$"},{"id":"d","text":"$$x \\in (2, 4)$"}],"correct_ids":["a"],"solution":"**Step 1:** Domain: $x^2 - 2x > 0 \\implies x(x-2) > 0 \\implies x < 0$ or $x > 2$.\n\n**Step 2:** Solve $x^2 - 2x < 2^3 = 8 \\implies x^2 - 2x - 8 < 0$.\n\n**Step 3:** Factor: $(x-4)(x+2) < 0 \\implies -2 < x < 4$.\n\n**Step 4:** Intersecting the domain and the solution: $(-2, 0) \\cup (2, 4)$.","created_at":"2026-06-07T01:38:55.439468+00:00","updated_at":"2026-10-14T04:36:26.526458+00:00","diagram_svg":null,"human_approved":false,"user_approved":false,"ai_approved":false,"ai_review":null,"topic":{"name":"Inequalities","slug":"algebra_inequalities","description":"Linear, quadratic, absolute value inequalities"}},"user":null,"initialGuestCount":0}]}]]}] f:[["$","meta","0",{"name":"viewport","content":"width=device-width, initial-scale=1"}],["$","meta","1",{"charSet":"utf-8"}],["$","title","2",{"children":"Ononot — Which values of x satisfy \\log2(x^2 - 2x) < 3?"}],["$","meta","3",{"name":"description","content":"Which values of x satisfy \\log2(x^2 - 2x) < 3?"}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","link","5",{"rel":"canonical","href":"https://ononot.com/questions/which-values-of-x-satisfy-log_2x2-2x-3-cfwhu"}],["$","meta","6",{"property":"og:title","content":"Ononot — Which values of x satisfy \\log2(x^2 - 2x) < 3?"}],["$","meta","7",{"property":"og:description","content":"Which values of x satisfy \\log2(x^2 - 2x) < 3?"}],["$","meta","8",{"property":"og:url","content":"https://ononot.com/questions/which-values-of-x-satisfy-log_2x2-2x-3-cfwhu"}],["$","meta","9",{"property":"og:type","content":"website"}],["$","meta","10",{"name":"twitter:card","content":"summary"}],["$","meta","11",{"name":"twitter:title","content":"Ononot — Which values of x s

Which values of xxx satisfy log⁡2(x2−2x)<3\log_2(x^2 - 2x) < 3log2​(x2−2x)<3?

Which values of $x$ satisfy $\log_2(x^2 - 2x) < 3$ ?