Mathematics July 22, 2026 · 10 min read

Condensing Logarithms: Combining Log Terms into One

Learn to condense logarithmic expressions using product, quotient, and power rules. Step-by-step examples included.

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Condensing logarithms means combining multiple logarithmic terms into a single logarithm. This skill is essential for solving equations, simplifying calculus operations, and analyzing mathematical expressions.

The Three Rules

  • Product Rule: log(A) + log(B) = log(AB)
  • Quotient Rule: log(A) - log(B) = log(A/B)
  • Power Rule: n × log(A) = log(Aⁿ)

Worked Example

Condense 2log(3) + log(5):

  1. Apply power rule: 2log(3) = log(9)
  2. Apply product rule: log(9) + log(5) = log(45)
  3. Result: log(45)