Change of Base Formula Logarithm Worksheet | Algebra 2 & Pre-Calculus Practice

Looking for a rigorous, no-prep way to teach or reinforce logarithm laws? This 20-problem Laws of Logarithms: Change of Base Worksheet is perfect for A-Level Maths and GCSE Higher Tier extension students. Featuring a dedicated section for evaluating complex logarithms completely by hand, this resource builds deep algebraic fluency and includes a complete, fully worked mark scheme for stress-free marking.

Give your advanced mathematics students the targeted practice they need to master the change of base formula and evaluate complex logarithms with absolute ease!
This Laws of Logarithms: Change of Base Worksheet is a comprehensive, no-prep resource specifically engineered for Year 11 (Higher Tier Extension), Year 12, and Year 13 A-Level Maths classrooms. It shifts students from passive formula memorisation to true algebraic mastery by challenging them across multiple styles of logarithmic evaluation.

What’s Included in This Resource?
• 1 Printable Student Worksheet: 20 meticulously scaffolded problems divided into distinct skill-building sections (rewriting into base-10 common logs, evaluating without a calculator, and simplifying advanced logarithmic quotients).
• Fully Worked Mark Scheme: A detailed solutions guide that shows every intermediate step—including power law adjustments, base changes, and index simplifications—making teacher marking rapid or allowing students to self-assess.

Skills Covered & Section Breakdown:
• Section 1 (Rewriting Logs): Rewriting equations into equivalent expressions using only base-10 common logarithms.
• Section 2 (Evaluating Expressions): Calculating values without a calculator using logical base transformations (e.g., matching bases to properties of 2, 3, or 5).
• Section 3 (Advanced Fractions): Simplifying complex fractions containing multiple log expressions across completely different bases.

Perfect For:
• Independent Practice / Homework: Solidify your daily lecture with a high-quality independent task.
• A-Level Exam Preparation / Revision: Perfect for reinforcing non-calculator skills and numerical stamina required on core algebra modules.
• Maths Lesson Starters or Exit Tickets: Pull a handful of problems for targeted warm-ups throughout 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.
• b Provides the perfect stretch and challenge material for top-set pupils preparing for Further Maths or bridging the gap to AS-Level.