Math lesson plan · 12th grade (Year 13 in England) · 30 minutes
Evaluate logarithms with the change-of-base formula
Algebra
CCSS HSF.LE.A.4England: A-level Pure Mathematics
Objective and success criteria
Students will: Evaluate logarithms with the change-of-base formula.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Evaluate logarithms without a calculator
Leads to: the next skill in this area.
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Evaluate logarithms without a calculator). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Evaluate log₅ 25. → 2Prompt: log₅ N asks: 5 to what power gives N?
- Evaluate log₃ (1/27). → -3Prompt: A fraction 1/bⁿ is b to a negative power.
- Evaluate log₉ 3. Give a fraction if needed. → 1/2Prompt: Write both numbers as powers of 3.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Evaluate logarithms with the change-of-base formula. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Use the change-of-base formula to evaluate log₇ 114 to 3 decimal places.
- Step 1: log 114 ÷ log 7 ≈ 2.434
- Answer: 2.434
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Use the change-of-base formula to evaluate log₅ 12 to 3 decimal places. → 1.544Prompt: log_b a = log a ÷ log b (any base, e.g. 10 or e).
- Without a calculator, log₅ 172 lies between two consecutive whole numbers. What is the smaller one? → 3Prompt: List powers of 5: 5, 25, 125, 625, …
You do: independent practice · 7 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Without a calculator, log₂ 253 lies between two consecutive whole numbers. What is the smaller one? → 7Prompt: List powers of 2: 2, 4, 8, 16, …
- Use the change-of-base formula to evaluate log₃ 96 to 3 decimal places. → 4.155Prompt: log_b a = log a ÷ log b (any base, e.g. 10 or e).
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Evaluate logarithms without a calculator.
- Use concrete materials: balance scales or a balance drawing.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-12.
Free lesson plan from eurekami.com/lesson-plan-builder