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Pre-Calculus

Pre-Calculus. Chapter 3 Exponential and Logarithmic Functions. 3.4 Solving Exponential and Logarithmic Equations. Objectives: Solve simple exponential and logarithmic equations. Solve more complicated exponential equations. Solve more complicated logarithmic equations.

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Pre-Calculus

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  1. Pre-Calculus Chapter 3 Exponential and Logarithmic Functions

  2. 3.4 Solving Exponential and Logarithmic Equations Objectives: • Solve simple exponential and logarithmic equations. • Solve more complicated exponential equations. • Solve more complicated logarithmic equations. • Use exponential and logarithmic equations to model and solve real-life problems.

  3. Change-of-Base Formula • Used to convert a log from one base to another. • To convert from base a to base b:

  4. Change-of-Base Formula • Most commonly used to convert a log to base 10 or to natural log for calculator use. • To convert from base a to base 10: • To convert from base a to natural log:

  5. Examples • Solve each by converting to common log and then using your calculator. • Solve again by converting to natural log. How do the answers compare?

  6. Properties of Logarithms

  7. Properties of Natural Logs

  8. Examples • Write each logarithm in terms of ln 2 and ln 3.

  9. Using the Properties • Properties of logs are used to rewrite logarithmic expressions, specifically to expand or condense them. • Expand – Take a single, complicated log expression and write it as several simple log expressions. • Condense – Take several simple log expressions and write them as one log expression.

  10. Examples – Expanding Expressions • Use the properties of logarithms to expand each expression.

  11. Examples – Condensing Expressions • Use the properties of logarithms to condense each expression.

  12. Additional Examples • Given f (x) = lnx, determine whether each statement below is true or false. Justify your answer.

  13. Homework 3.3 • Worksheet 3.3 # 5, 11, 15, 23 – 61 odd, 67 – 79 odd, 82, 85 – 91 odd, 103, 105

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