Product and Power Properties of Logarithms Worksheet | Algebra 2 & Pre-Calculus

Looking for a rigorous, no-prep way to teach expanding and condensing logarithms? This comprehensive Laws of Logarithms: Product and Power Rules Worksheet is perfect for A-Level Maths and GCSE Higher Tier extension students. Featuring targeted sections on simplifying expressions and evaluating logarithms completely without a calculator, this resource includes a fully worked mark scheme for quick, stress-free marking.

This Laws of Logarithms: Product and Power Rules Worksheet is a comprehensive, no-prep resource engineered specifically for Year 11 (Higher Tier Extension), Year 12, and Year 13 A-Level Maths classrooms. It moves students past basic formulas into procedural fluency by targeting the product law (addition rule) and power law through progressive, scaffolded practice.
A standout feature of this worksheet is its explicit focus on non-calculator execution.

What’s Included in This Resource?
• 1 Printable Student Worksheet: Meticulously structured practice sections (writing multiple terms as a single logarithm, simplifying expressions with powers, and evaluating composite products).
• Fully Worked Mark Scheme: A detailed solutions guide showing exactly how expressions are condensed and broken down into base-power pairs for easy teacher marking or student self-assessment.

Skills Covered & Section Breakdown:
• Section 1 (Condensing Logarithms): Using the product law to condense expressions with the same base into a single logarithm.
• Section 2 (Evaluating Power Rules): Using the power law to hand-calculate numeric logarithm indices without a calculator.
• Section 3 (Composite Products): Evaluating complex expressions containing products and powers (e.g. simplifying log base 4 of 16 multiplied by 64).

Perfect For:
• Independent Practice / Homework: Give your students high-quality, independent reinforcement after your daily lecture.
• A-Level Exam Preparation / Revision: Excellent for building the fast-paced non-calculator stamina needed for advanced algebraic modules.
• Maths Lesson Starters or Exit Tickets: Pull a handful of problems for quick, targeted warm-ups during your indices and logarithms unit.
• Hassle-Free Cover Lessons: No technology or special graphical calculators required—just print, copy, and hand out!

Curriculum Alignment:
• UK A-Level Maths Framework: Aligns directly with pure mathematics requirements across AQA, Edexcel, OCR, and WJEC specifications regarding the laws of logarithms.
• **GCSE Higher Tier (Year 11 Extension): **Provides the perfect stretch and challenge material for top-set pupils preparing for Further Maths courses.