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Lesson 6.3: Logarithmic Functions

6. 3 Logarithmic Functions Objectives: Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic functions to solve equations. Standard: 2.8.11.S. Analyze properties and relationships of functions. Lesson 6.3: Logarithmic Functions.

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Lesson 6.3: Logarithmic Functions

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  1. 6. 3 Logarithmic FunctionsObjectives: Write equivalent forms for exponential and logarithmic equations.Use the definitions of exponential and logarithmic functions to solve equations.Standard: 2.8.11.S. Analyze properties and relationships of functions. Lesson 6.3: Logarithmic Functions

  2. Warm Up:

  3. Logarithms are used to find unknown exponents in exponential models. LogarithmicFunctionsdefine many measurement scales in the sciences, including the pH, decibel, and Richter scales.

  4. With logarithms, you can write an exponential equation in an equivalent logarithmic form.

  5. You can evaluate logarithms that have a base of 10 by using the key on a calculator . log

  6. p. 374 #4 – 7

  7. The inverse of the exponential function y = 10x is x = 10y. To rewrite x = 10y in terms of y, use the equivalent logarithmic form, y = log 10 x.

  8. The logarithmic function y = log x with base b, or x = by, is the inverse of the exponential function y = bx, where b ≠ 1 and b > 0. One-to-one Property of Exponents If bx = by, then x = y.

  9. “TRY THIS” top 373 a. v = 3 b. v = 5 c. v = 729

  10. The function is used in chemistry to measure pH levels. The pH of a solution describes its acidity. Substances that are more acidic have a lower pH, while substances that are less acidic, or basic, have a higher pH. The pH of a substance is defined as pH = -log10 [H+], where [H+] is the hydrogen ion concentration of a solution in moles per liter.

  11. Try These: p. 374 #8 - 11

  12. Homework: Practice 6.3 Quiz on Lessons 6.1 – 6.4 This Friday

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