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A logarithm answers the question: "To what power must the base be raised to get this number?" log_b(x) = n means bⁿ = x. Logarithms compress enormous ranges and are used in sound (decibels), earthquakes (Richter scale), and pH.

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1. 1log_b(x) = n means bⁿ = x
2. 2Common log (log₁₀): log(1000) = 3 because 10³ = 1000
3. 3Natural log (ln): ln(e) = 1 because e¹ = e ≈ 2.718
4. 4log_b(x) = log(x)/log(b) — change of base formula

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