Algebra II Lesson

Solving Exponential & Logarithmic Equations: From Form Fluency to Financial Modeling

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11th Grade — Level III (Honors)BTC Style / Thinking Classrooms50 min

Learning Objective

Students will solve exponential and logarithmic equations by leveraging the inverse relationship between exponential and logarithmic forms, applying properties of logarithms, and interpreting solutions in real-world contexts including compound interest and radioactive decay.

Lesson Overview

Students progress from converting between exponential and logarithmic forms through solving equations algebraically, then apply skills to compound interest and half-life contexts. Instruction is anchored in conceptual equivalence before procedural tools are introduced.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors)
Pencils and scratch paper
Basic scientific calculator (phone calculator acceptable)

Scaffolded Task Progression

1Task 1

Rewrite each equation in the other form (exponential ↔ logarithmic). No solving required — just translate.
a)

2^{5} = 32

lo g_{3} 81 = 4

1 0^{x} = 1000

lo g_{5} x = 3

2Task 2

Solve each equation by converting to the other form first. Show the conversion step explicitly.
a)

lo g_{4} x = 3

2^{x} = 64

lo g_{x} 27 = 3

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