# Exponents & Logs

**Essential Question: How do we model and use exponential growth and decay?**

__Powers with Rational Exponents__

**1) Evaluate Powers with Rational Exponents**

- Explanation:
- Notes | Annotated Notes
- Video:
- Khan: Introduction to rational exponents
- Khan: Rewriting roots as rational exponents
- Khan: Radicals and exponents (ignore the last problem)
- Khan: Evaluating rational exponents: negative unit-fraction
- Khan: Evaluating rational exponents
- Khan: Evaluating rational exponents: rational base
- Review of negative exponents (optional review):

- Practice Problems:
- Worksheet #1 | Answers
- Worksheet #2 | Answers
- Khan exercise: Negative exponents
- Khan exercise: Rational exponents: unit fractions
- Khan exercise: Rational exponents and radicals

- Teacher Resources:
- ExamView Test Bank (purchase)

**2) Operations of Powers with Rational Exponents**

- Explanation:
- Practice Problems
- Worksheet #1 | Answers
- Worksheet #2 | Answers
- Worksheet #3
- Khan exercise: Properties of exponents (rational exponents)

- Khan exercise: Multi-step simplification of rational exponent expressions
- Khan exercise: Equivalent forms of exponential expressions
- Teacher Resources:
- ExamView Test Bank (purchase)

**3) Simplify Roots**

- Explanation
- Practice Problems
- Worksheet

**4) Solve Equations with Fractional Exponents (Root Equations)**

- Explanation:
- Practice Problems
- Worksheet #1 | Answers
- Worksheet #2 | Answers
- Teacher Resources:
- ExamView Test Bank (purchase)

__Exponential Equations__

**5) Solve Equivalent Powers with the Same Base**

- Explanation:
- Practice problems:
- Worksheet #2
- Worksheet #3
- Teacher Resource:
- ExamView Test Bank (purchase)

__Logarithmic Expressions__

**6) Simplify Single Logs (including natural log) & Inverse Properties**

- Explanation:
- Notes | Annotated
- Khan video: Introduction to Logarithms
- Khan text: Intro to Logarithms
- Khan video: Evaluating logarithms (advanced)
- Khan video: Relationship between exponentials & logarithms
- Khan video: e as a limit
- Khan video: How to evaluate a natural logarithm using a calculator (example)

- Practice Problems:
- Worksheet #3
- Worksheet #4
- Khan Exercise: Evaluate logarithms (basic)
- Khan Exercise: Evaluate logarithms (advanced)
- Quizlet Scatter: review inverse operations

- Teacher Resources:
- ExamView Test Bank (purchase)

**7) Property of Logs: Combine & Expand Logs**

- Explanation:
- Notes | Annotated
- Khan video: Introduction to Logarithm properties (adding and subtracting logs)
- Khan video: Introduction to Logarithm properties (part 2) (multiplying logs by a number)
- Khan text: Intro to logarithm properties
- Khan video: Using the logarithmic product rule
- Khan video: Using the logarithmic power rule (power of a log)
- Khan video: Using the properties of logarithms: multiple steps
- Khan text: Justifying the logarithm properties
- Khan video: Proof of the logarithm product rule
- Khan video: Proof of the logarithm quotient and power rules

- Practice Problems:
- Worksheet #2
- Khan exercise: Use the properties of logarithms

- Teacher Resource
- ExamView Test Bank (purchase)

**8) Approximate Logs by Expansion**

- Exercises:
- Worksheet #1
- Worksheet #2

**9) Use the Change of Base Formula to find the decimal approximation of a log**

- Explanation:
- Notes | Annotated
- Khan video: Evaluating logarithms: change of base rule
- Khan text: Logarithm change of base rule intro
- Khan video: Using the logarithm change of base rule
- Khan video: Change of base formula proof
- Khan text: Logarithm properties review

- Practice Problems:
- Worksheet #2
- Teacher Resource:
- ExamView Test Bank (purchase)

__Solve Logarithmic Equations__

**10) Solve Logarithmic Equations (with one log):**

- Explanation:
- Video
- Practice Problems:
- Worksheet #2
- Teacher Resource:
- ExamView Test Bank (purchase)

**11) Solve Logarithmic Equations When There is More than One Log**

**E**xplanation- Practice Problems:
- Teacher Resource
- ExamView Test Bank (purchase)

__Solving Exponential Equations__

**12) Solve Exponential Equations when the bases are not the same**

- Explanation
- Practice Problems:
- Worksheet #2
- Teacher Resources:
- ExamView Test Bank (purchase)

13) **Solve Exponential Equations when the bases are not the same and there is more than one variable**

- Explanation:
- Practice Problems:

**14) Solve Exponential Equations by factoring**

- Explanation
- Practice Problems

**15) Review of Exponential and Logarithmic Expressions and Equations:**

**16) Cumulative Review WS**