Three worksheets on the following basic properties of logarithms:

• log_a 1=0
• log_a a=1
• log_a a^x=x
• a^{log_a x}=x
• product rule
• division rule
• power rule/exponential rule
• change of base rule
  Detailed solutions are included.

Looking for the ultimate, ready-to-use revision collection to help your students master logarithms? This comprehensive 3-worksheet bundle covers everything from basic evaluation and nested logarithms to advanced expansion, condensation, and algebraic proofs. Best of all, it includes 15 full pages of detailed, step-by-step worked solutions to save you hours of marking time!

The Ultimate Laws of Logarithms Practice & Revision Bundle!
Give your students a flawless foundation in logarithms with this comprehensive, ready-to-print worksheet bundle. This complete resource package merges three distinct, scaffolded practice sets, making it perfect for A-Level Mathematics, Core Maths, Advanced Higher, and upper secondary maths students preparing for upcoming algebra exams, assessments, or end-of-term mocks.
Designed for high utility with zero teacher preparation required, this bundle provides a logical progression from core conceptual definitions to advanced algebraic manipulation.

What is Included in This Bundle?
Resource 1: Basic Properties of Logarithms
• 30 Scaffolded Problems focusing on evaluating expressions without a calculator.
• Covers foundational base identity laws, powers, fractional inputs, and large base-10 indices.
• Features advanced nested logarithms (such as evaluating log base 2 of log base 5 of 25) to push higher-order critical thinking.
Resource 2: Laws & Properties of Logarithms
• 8 Multi-Part Problem Sets focused on practical law application.
• Evaluating Expressions: Using product, quotient, and power properties to simplify numeric values.
• Expressing as a Single Logarithm (Condensing): Rewriting multi-step variable expressions into single structures.
• Variable Expansion: Rewriting complex algebraic and radical inputs strictly in terms of given variables (a and b).
• Change of Base & Verifications: 8 targeted identity proofs where students mathematically verify logarithmic equivalence.
Resource 3: Laws of Logarithms (Deep-Dive Revision)
• Focuses heavily on the mechanics of writing expressions as a single logarithm and simplifying.
• Introduces fractional index manipulation, roots, fractional dividers, and multi-variable expansion models.
• Perfect for a second day of mastery practice, homework assignments, or a comprehensive unit revision guide.

Complete Step-by-Step Answer Keys Included
Every single problem across all three resources features a dedicated, line-by-line worked solution. It shows every mathematical transition, index law application, and base change. This makes the bundle ideal for student self-assessment, independent study, or instantaneous teacher marking.

Why Teachers Love This Bundle:
• Ready to Teach: Just print the pages you need and pass them out! An instant addition to your curriculum.
• Perfectly Scaffolded: Students build structural confidence on basic evaluations before transitioning into complex variable expansion and algebraic proofs.
• Highly Versatile: Use it for direct classroom instruction, independent homework, exam revision packets, or emergency cover work.