Subject: Mathematics
Book: Maths Mastery
Log inequalities like log(x) > 2 or log₂(x–1) ≤ 3 require understanding domain (x>0 for log base 10, x–1>0 for log₂) and exponential transformations. For log(x)>2, rewrite as x>10²=100. Solve carefully, checking intervals against log domain constraints. More complex expressions may involve combining log properties or adding constants. Log inequalities arise in pH ranges, decibel thresholds, or exponential growth constraints. Systematic approach ensures correct intervals, avoiding extraneous solutions from domain missteps.
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