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Key Concepts
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1. Definition
If aʸ = x, then logₐ x = y (where a > 0, a ≠ 1).
2. Laws of Logarithms
- Product Rule: logₐ (MN) = logₐ M + logₐ N
- Quotient Rule: logₐ (M/N) = logₐ M - logₐ N
- Power Rule: logₐ (Mᵏ) = k · logₐ M
- Change of Base: logₐ M = (logₓ M) / (logₓ a)
3. Common vs Natural Logs
- Common Log: Base 10 (log x)
- Natural Log: Base e (ln x)