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Mastering Logarithmic Functions: Properties, Graphs, and Applications

Explore logarithmic functions and their properties, including rewriting logarithms, graphing techniques, and real-world applications such as mortgage calculations. Understand the nature of logarithms and their relation to exponential functions. Learn about transforming and graphing logarithmic functions effectively.

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Mastering Logarithmic Functions: Properties, Graphs, and Applications

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  1. Pg. 293/301 Homework • Pg. 301#23 – 51 odd • #29 3log2x + 2log2y #31 2logax – 3logay • #33 log5000 + log x + 360log(1+r) #35 Graph • #37 Graph #39 f(x) → 1, f(x) → 1 • #41 f(x) → 1, no Left EB #1 D: (0, ∞); R: (-∞, ∞) • #3 D: (0, ∞); R: (-∞, ∞) #5 D: (0, ∞); R: (-∞, ∞) • #7 Graph #9 x = -5 • #11 x = 2 #13 x = -3/2 • #15 x = 4 #17 D: (0.5, ∞); R: (-∞, ∞) • #19 D: (-∞, 3); R: (-∞, ∞)

  2. 5.3 Effective Rates and Annuities • A $250,000 mortgage for 30 years at 6% APR. What will the monthly payments be? • Suppose you make the required monthly payments for that same $250,000 mortgage for 12 years and then make payments of $3500.00 until the loan is paid. In how many years total will the mortgage be completely paid?

  3. 5.4 Logarithmic Functions and Their Properties Properties

  4. 5.4 Logarithmic Functions and Their Properties Rewrite the following Logarithms The Nature of Logarithms Why do we deal with positive x values when dealing with logs? What information do we always know about a log? What does the parent function of a log look like? Compare that to the parent function of an exponential.

  5. 5.5 Graphs of Logarithmic Functions Graphing Logarithms Prove it! • In order to graph a logarithm in your calculator, you must use the change of base formula:

  6. 5.5 Graphs of Logarithmic Functions Transitions Graph the following Logarithms State the transitions and/or reflections that occur and the domain and range. • The graph of any logarithmic function of the form y = alogb(cx + d) + kcan be obtained by applying geometric transformations to the graph of y = logbx

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