Math lesson plan · 11th grade (Year 12 in England) · 45 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 · 5 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 log₅ 125 = 3 in exponential form. (125^3 = 5 / 5^3 = 125 / 5^125 = 3 / 3^5 = 125) → 5^3 = 125Prompt: bˣ = N means the same as log_b N = x.
- log 3 + log 2 − log 3 = log N. Find N. → 2Prompt: Adding logs multiplies the numbers; subtracting divides.
- Solve log₂ x = 0. → 1Prompt: Rewrite in exponential form.
Hook · 5 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 · 10 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 · 10 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(5x + 4) = 2. → x = 1Prompt: Rewrite in exponential form.
- Solve log₃ x + log₃(x − 2) = 1. → 3Prompt: Combine into one logarithm, then remove the log.
You do: independent practice · 10 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 · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Solve log₃(4x − 7) = 2. → x = 4Prompt: Rewrite in exponential form.
- Solve log₂ x + log₂(x + 1) = 1. → 1Prompt: Combine into one logarithm, then remove the log.
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