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A logarithm is the inverse of exponentiation. log_b(x) answers "to what power must b be raised to get x?" Common logarithm (base 10) is used in science; natural logarithm (base e) in calculus; binary logarithm (base 2) in computer science.

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1. 1log_b(x) = n means b^n = x
2. 2Common log: log₁₀(1000) = 3 because 10³ = 1000
3. 3Natural log: ln(e) = 1 because e^1 = e
4. 4Change of base: log_b(x) = log(x) / log(b)

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