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Laws of logarithms worksheet (with solutions)

Laws of logarithms worksheet (with solutions)

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

5 August 2026

pdf, 121.01 KB
pdf, 121.01 KB

A worksheet on using the three basic laws of logarithms (adding logarithms with the same base, subtracting logarithms with the same base and simplifying the logarithm of a power). Detailed solutions are included. Good for A level students.

Get this resource as part of a bundle and save up to 43%

A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

Bundle

Laws & Properties of Logarithms Practice Worksheets Bundle - No Prep | Algebra 2

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. ________________________________________

£3.65
Bundle

Exponentials and logarithms Bundle

A collection of four worksheets on the following topics: writing expressions as a logarithm, laws of logarithms, changing the base of logarithms and solving exponential equations. Detailed solutions are included. Good for A level students.

£3.90
Bundle

Logarithms Bundle

A collection of three worksheets on logarithms. An introductory worksheet on logarithms with exercises that require converting expressions from exponential to logarithmic form and evaluating given logarithms, a worksheet on equations with logarithms and a worksheet on using the three basic laws of logarithms (adding logarithms with the same base, subtracting logarithms with the same base and simplifying the logarithm of a power). Detailed solutions are included.

£3.35
Bundle

Laws of logarithms Bundle

A collection of three worksheets on special cases of logarithms and the three basic laws of logarithms (adding logarithms with the same base, subtracting logarithms with the same base and simplifying the logarithm of a power). Detailed solutions are included. Good for A level students.

£3.35
Bundle

Changing the base of a logarithm-Laws of logarithms Bundle

A collection of three worksheets. Two worksheets on changing the base of a given logarithm and evaluating or simplifying expressions by changing the base of a logarithm and one worksheet on using the three basic laws of logarithms (adding logarithms with the same base, subtracting logarithms with the same base and simplifying the logarithm of a power). Solutions are included.

£3.35

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