• 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.

1. Write log₃ 9 = 2 in exponential form. (3^9 = 2 / 2^3 = 9 / 3^2 = 9 / 9^2 = 3) → 3^2 = 9Prompt: bˣ = N means the same as log_b N = x.
2. log 5 + log 3 − log 5 = log N. Find N. → 3Prompt: Adding logs multiplies the numbers; subtracting divides.
3. Solve log_b 5 = 1 for the base b. → 5Prompt: Rewrite as b^n = N.

• 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.

• 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.

• Do these together. Students try each step on whiteboards before you reveal it.
• Use the hints as prompts rather than giving the answer.

1. Solve log₅(2x + 3) = 2. → x = 11Prompt: Rewrite in exponential form.
2. Solve log₂ x + log₂(x + 6) = 4. → 2Prompt: Combine into one logarithm, then remove the log.

• 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.

• Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.

1. Solve log₃(5x + 2) = 3. → x = 5Prompt: Rewrite in exponential form.
2. Solve log₁₀ x + log₁₀(x + 117) = 3. → 8Prompt: Combine into one logarithm, then remove the log.

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-11.