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Verified answer
³log(x²-2x) < 3³log(x² - 2x) < ³log3³
x² - 2x < 3³
x² - 2x < 27
(x - 1)² - 1 < 27
(x - 1)² < 28
-√28 < x - 1 < √28
-√28 + 1 < x < √28 + 1
-2√7 + 1 < x < 2√7 + 1