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Logarithms Teacher Resources
A complete set of teacher resources for teaching logarithms in senior maths. Covers the relationship between exponential and logarithmic form, the log laws (product, quotient and power), change of base, and solving logarithmic equations. Includes lesson plans, worksheets, slide decks, question banks, and assessments you can use straight from the file.
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What's included in the logarithms resources
🔥Curriculum Aligned
Lesson plans that build from the exponential-logarithm relationship to the log laws, change of base, and solving log equations. Each lesson includes worked examples, board prompts, and a clear sequence of practice so students see why log b(x) is the inverse of b to the power of x.
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🌍 Differentiated for Students
Real-world hooks students recognise: the Richter scale for earthquakes, decibels for sound intensity, pH in chemistry, and compound interest in finance. Each application is set up so students can move between the contextual story, the equation, and the answer without losing the meaning.
💡Incredible Teacher Resources
Extension questions push students from procedural fluency into proof and reasoning: deriving the change of base formula, justifying the log laws from index laws, and interpreting why logarithmic scales are used. A clear set of stretch tasks for the students who finish early.
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Interactive Resources
Practice Questions
Step-by-step solutions for converting between exponential and logarithmic form, simplifying log expressions with the product, quotient and power rules, applying change of base, and solving equations of the form log b(x) = c and b to the power of x = c. Students see the reasoning, not just the answer.
Structured Solutions
Differentiated Questions
Worksheets and question banks scaffold from one-step substitution through to multi-step equations and exam-style problem solving. Differentiation is built in so a class with mixed entry points can all start, all stretch, and finish with the same core understanding of logarithms.
Real-World Applications
Engaging Exercises
Tasks use the contexts senior students actually meet in exams and in life: earthquake magnitudes, sound levels in decibels, the pH scale, half-life and radioactive decay, and continuous compounding. Worked solutions show the modelling step and the algebra side-by-side.
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What is covered in the logarithms resources
Introducing logarithms and the exponential link
The log laws and change of base
Real-world applications of logarithms
The introduction sequence positions a logarithm as the inverse of an exponential. Students convert between the exponential form b to the power of x = y and the logarithmic form log b(y) = x, with worked examples in base 10, base e, and arbitrary bases. The lesson plans include diagnostic prompts so teachers can quickly read which students are confident with the index laws and which need a brief recap before pushing on.
The middle of the unit covers the three log laws — product, quotient, and power — alongside the change of base formula. Students learn to simplify expressions like log(8) + log(5), expand log(x squared y), and rewrite log base 2 of 30 using the change of base formula. The worksheets and question banks scaffold from substitution into multi-step problems and into the kind of equations students meet in senior exams.
The application sequence connects logarithms to the situations students hear about outside the classroom. Earthquake magnitudes on the Richter scale, sound intensity in decibels, pH in chemistry, half-life in radioactive decay, and continuous compound interest all use logarithmic models. The lesson plans walk through how to set up the equation, solve it, and read the answer back into the original context.
Teachers save hours with the logarithms resources