A worksheet 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
The exercises require the use of these properties to evaluate expressions without the use of a calculator. Detailed solutions are included.
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Logarithms Worksheet Bundle | Properties, Laws, Change of Base & Equations
A collection of four worksheets on logarithms. The following worksheets are included: * Basic properties of logarithms * Addition and power laws of logarithms * Laws of logarithms * Changing the base of logarithms Solutions are provided. Master logarithmic laws and equations with this complete A-Level Maths worksheet bundle! Perfectly optimized for Year 12 and Year 13 Pure Mathematics revision, this pack covers basic log properties, expanding, condensing, change of base, and solving complex log equations with full worked solutions. Looking for a comprehensive, print-and-go resource pack to help your sixth-form students confidently master logarithms? This Laws of Logarithms Mastery Worksheet Bundle contains a highly structured collection of problems designed to build calculation fluency and deep analytical confidence. Moving from basic non-calculator rules and multi-term simplifications to complex expansion indices and algebraic equations that turn into quadratic factors, this resource is perfect for daily secondary lessons, independent revision booklets, structured homework assignments, cover work, or university preparation! Every page is uncrowded and comes accompanied by a complete, step-by-step worked answer key making marking quick and straightforward for busy teachers or peer assessment. **What's Included in This Bundle?** • **Basic Properties of Logarithms:** Non-calculator evaluations introducing fractional tracking and nested expressions. • **Addition and Power Laws:** Exercises for writing multiple log expressions as a single term, alongside evaluating numerical strings. • **Expansion of Logs:** Writing complex composite equations explicitly in terms of log_a(x), log_a(y), and log_a(z) using rules of division and roots. • **Changing the Base & Solving Equations:** Using change of base laws to evaluate decimal values alongside working out algebraic equations using quadratic substitution (such as setting log_a(x) equal to y). **Perfect For:** • AS & A-Level Mathematics: Targeted Pure Maths practice for Year 12 and Year 13 students securing core algebra marks. • IB Diploma & Further Maths: Rigorous algebraic manipulation training for advanced algebraic tracks. • Cover Work & Homework Extensions: Structured layouts requiring zero prep work from you or a supply teacher.
£3.95
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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
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