Lesson Plan

• Describe the relationship between exponential and logarithmic forms.
• Apply the logarithmic method to solve a^x = b for any positive a ≠ 1 and b > 0.
• Choose and use an appropriate logarithm base (common, natural, or base‑a) to isolate x.
• Check solutions for validity and express answers with the correct number of significant figures.
• Solve simple cases without logarithms by matching exponents or using a graphical approach.

• Projector and screen
• Whiteboard and markers
• Student worksheets with practice questions
• Scientific calculators
• Printed handout of key logarithm formulas
• Graph paper

Begin with a quick puzzle: “If 3^x = 81, what is x?” Students answer using prior knowledge of powers. Review that the inverse of an exponential function is a logarithm and state the success criteria: students will be able to rewrite a^x = b as x = log_ab and solve it accurately.

1. Do‑now (5′): Mini‑whiteboard activity solving 3^x=81; teacher checks understanding of the power rule.
2. Mini‑lecture (10′): Present the exponential ↔ logarithmic relationship, derive x = log_ab, and illustrate with common logarithms.
3. Guided practice (12′): Work through the natural‑log example (5^x=0.2) step‑by‑step; students fill in missing steps on their worksheets.
4. Independent practice (15′): Students attempt Questions 1‑4 from the worksheet; teacher circulates, prompting use of the general procedure.
5. Alternative methods (8′): Demonstrate a quick graphical solution using the projector and a graphing calculator.
6. Check for understanding (5′): Exit ticket – students write the five‑step procedure in their own words.

Summarise the key steps for solving a^x = b and remind students of common pitfalls such as forgetting domain restrictions. Collect the exit tickets to gauge mastery, and assign homework: complete the remaining practice questions and sketch a graph to verify one solution.