Subject: Mathematics
Book: Maths Mastery
Exponential inequalities, like 2^x > 10 or 3^(x–1) ≤ 27, often require taking logarithms or rewriting terms. For 2^x > 10, x>log₂(10), so x> ~3.3219. Alternatively, if 3^(x–1)≤27, note 27=3³, so x–1≤3 → x≤4. Watch for sign flips if the base is between 0 and 1 (like (1/2)^x). These inequalities apply to population bounds, decay processes, or resource management. Mastering exponential inequalities fosters confident handling of wide-ranging growth/decay constraints in scientific, financial, or engineering domains.
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