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Exploring Logarithmic Functions: Recognize, Evaluate, and Graph

Dive into how to identify, assess, and plot logarithmic functions. Understand their properties and transformations compared to other function types. Learn new vocabulary and practice evaluating logarithms with real examples. Don't miss out on exploring natural logarithmic functions. Homework assignments provided for further practice.

hoshiko-miyamoto
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Exploring Logarithmic Functions: Recognize, Evaluate, and Graph

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  1. Warm Up • Make a t-chart for the following functions • 3x • 3-x • 3x + 1

  2. Math IV Lesson 16 Essential : How do you recognize, evaluate, and graph logarithmic functions? Standard: a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise. b. Investigate transformations of functions

  3. New Vocabulary • Logarithmic form: logba = c • Exponential form: bc = a • Logarithmic function: f(x) = logax • Natural logarithmic function: f(x) = ln(x)

  4. Changing between log form and exponential form We all know 32 = 9 Now lets write it in log form…..

  5. Evaluating logs Solve for x (hint put in exponential form) • log232 = x • Log31 = x • Log42 = x

  6. Properties of logs • loga1 = 0 • Logaa = 1 • Logaax = x • If logax = logay , then x = y

  7. Examples • Solve for x Log2x = log23 Simplify log55x Solve for x Log44 = x

  8. Graphs of logs and exponential equations • Graph both Y = 2x and y = log2x

  9. Natural log ln • F(x) = logex = ln(x) Properties of natural logs • ln1 = 0 because e0 = 1 • Ln (e) = 1 because e1 = e • Lnex = x because elnx = x • If ln(x) = ln(y) then x = y

  10. Using properties of natural logs • Simplify the expressions Ln (1/e) eln5 4ln(1) 2ln(e)

  11. Home work • P203 • 1-17 odd, 25-28,

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