Math lesson plan · 11th grade (Year 12 in England) · 60 minutes
Solve logarithmic equations
Algebra
CCSS HSF.BF.B.5England: A-level Pure Mathematics
Objective and success criteria
Students will: Solve logarithmic equations.
- 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: Switch between exponential and logarithmic form; Combine logarithms into a single logarithm
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 · 6 min
- Quick retrieval from earlier learning (Switch between exponential and logarithmic form; Combine logarithms into a single logarithm). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Write 2^4 = 16 in logarithmic form. (log₂ 4 = 16 / log₂ 16 = 4 / log₁₆ 2 = 4 / log₄ 16 = 2) → log₂ 16 = 4Prompt: bˣ = N means the same as log_b N = x.
- log 11 + log 10 − log 2 = log N. Find N. → 55Prompt: Adding logs multiplies the numbers; subtracting divides.
- Solve log_b 5 = 1 for the base b. → 5Prompt: Rewrite as b^n = N.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve logarithmic equations. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Solve log₁₀(2x) = 2.
- Step 1: 2x = 100
- Step 2: x = 50
- Answer: x = 50
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Solve log₃(3x + 9) = 3. → x = 6Prompt: Rewrite in exponential form.
- Solve log₃ x + log₃(x − 6) = 3. → 9Prompt: Combine into one logarithm, then remove the log.
You do: independent practice · 17 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 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Solve log₁₀ x + log₁₀(x + 48) = 2. → 2Prompt: Combine into one logarithm, then remove the log.
- Solve log₂(2x + 8) = 2. → x = -2Prompt: Rewrite in exponential form.
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: Switch between exponential and logarithmic form.
- 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-11.
Free lesson plan from eurekami.com/lesson-plan-builder