A worksheet on equations with logarithms. It includes introductory and harder exercises on this topic. Some equations require to use the properties of logarithms to solve them. Detailed solutions are included. Good for A level students.

Looking for a rigorous, ready-to-use revision resource to help your students master solving advanced logarithmic equations? This printable maths worksheet features multi-part problem sets covering everything from basic log definitions to complex change of base questions and quadratic-form exponential equations. Best of all, it includes 12 full pages of detailed, line-by-line worked solutions to save you hours of marking time!

What is Included in This Resource?
• Section 1: Foundational Log Equations – Questions requiring students to apply basic logarithmic definitions to isolate the unknown variable (covers standard bases, fractional bases, and base-x questions).
• Section 2: Log Laws & Property Applications – Equations where students must use product and quotient laws to combine logarithmic terms before solving.
• Section 3: Advanced Polynomial & Substitution Forms – 12 rigorous equations including nested logarithms, fractional indices, substitution models, and quadratic-form logarithmic tracking (e.g., equations requiring students to let a change to 3 to the power of log x).
• Section 4: Change of Base Formula Tracking – 6 multi-step problems forcing students to manipulate terms with mismatched bases, convert roots, and identify structural constraints.
• Detailed Domain Verification & Extraneous Solution Checking – Unlike generic worksheets, the answer key explicitly writes out domain restrictions and demonstrates why negative or invalid values must be rejected.
• Complete Step-by-Step Answer Key – 12 full pages of line-by-line solutions showing every single algebraic transformation, property change, and quadratic factorising step, making it perfect for student self-assessment, independent study, or quick marking.

Why Teachers Love This Worksheet:
• Ready to Teach: Just print and go! It is an instant, complete lesson addition, homework assignment, or exam pack.
• Scaffolded Challenge: Problems move quickly from basic structural checks into premium, high-level critical thinking, ideal for stretching higher-tier students or preparing for exam-style questions.
• Versatile Use: Ideal for in-class independent practice, homework assignments, exam revision packets, or emergency cover work.