Logarithm is the inverse of exponentiation. If a^x = b, then log_a(b) = x (read as: log of b to base a equals x). Key concepts: Base: a (usually 10 or e); Argument: b (must be positive); Result: x (can be any real number). Common logarithm: log (base 10); Natural logarithm: ln (base e ≈ 2.718). Special values: log_a(a) = 1; log_a(1) = 0; log_a(a^n) = n. Example: log_2(8) = 3 because 2^3 = 8. Converting: If 10^x = 100, then x = log(100) = 2. Shortcut: Remember common log values (log 10 = 1, log 100 = 2). Exam tip: Logarithm arguments must be positive. Understand exponential-logarithmic relationship thoroughly.