A worksheet on evaluating logarithms using the change of base formula.

There are 20 problems and detailed solutions are included.

Looking for a rigorous, no-prep resource to help your students master the change of base property? This targeted practice worksheet is designed to build complete operational fluency, challenging students to evaluate and simplify logarithmic expressions entirely by hand without relying on a calculator!

Whether you need a focused homework task, a robust in-class practice set, revision stations, or a reliable cover plan, this resource has everything you need to deepen your students’ algebraic understanding.

What’s Included in This Resource:

• Evaluating Mismatched Bases: Includes core problems that require students to identify a common base and apply the Change of Base formula to evaluate terms (such as evaluating log base 9 of 27 or log base 125 of 25).
• Advanced Multi-Term Operations: Features challenging problems involving logarithmic fractions and products where students must apply the property to cross-cancel terms and simplify the expression (such as multiplying log base 5 of 16 by log base 2 of 25).
• Radical and Fractional Bases: Pushes student boundaries with fractions, fractional bases, and radical terms to ensure true concept mastery.
• Complete Step-by-Step Solutions: Full structural working out and numerical solutions are provided for every single problem to save you hours of marking time or to facilitate seamless student self-assessment.

Curriculum & Level Alignment:
This worksheet perfectly maps to higher-level secondary mathematics and senior secondary courses globally:

• UK Curriculum: Key Stage 4 (Higher GCSE) and AS/A-Level Mathematics (Pure Mathematics - Exponentials and Logarithms).
• Australian Curriculum: Year 11 & 12 Mathematical Methods (Unit 1/2 Functions & Graphs).
• International Curricula: IB Math (AA/AI SL & HL) and IGCSE Additional Mathematics.