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y. x. Warm-Up. Graph. Y – Int. (0,-1). HA: y = 3. Domain: All Real Numbers. Range: y < 3. CA Standards: 12.0 Students know the laws of fractional exponents, understand exponential functions, and use theses functions in problems involving exponential growth and decay.

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  1. y x Warm-Up Graph Y – Int. (0,-1) HA: y = 3 Domain: All Real Numbers Range: y < 3

  2. CA Standards: 12.0 Students know the laws of fractional exponents, understand exponential functions, and use theses functions in problems involving exponential growth and decay. Objective:(1) Graphing Exponential Growth Functions (2) Using Exponential Growth Models. Agenda: 03/02/15 1.) Warm-up 2.) Questions 3.) Lesson: 8.4 Properties of Logarithms 4.) Class/Homework TB 8.4 #’s 5 – 47 ALL

  3. Introduction 1) Graph: 2) Graph: (Dashed) 3) Switch the x & y in the table from step 1 and plot the new coordinates, sketch the new curve.

  4. 8.4 Logarithmic FunctionsGoal 1: Evaluating Logarithmic Functions The definition of a Logarithm with base b log by = x if and only if bx = y (MEMORIZE THIS RELATIONSHIP) • The expression log b y = x is called a LOGARITHMICForm • 2) The expression log b y = x is read “log base b of y” • 3) The expression y = b x is called an EXPONENTIAL Form

  5. 8.4 Logarithmic FunctionsContinued Ex.1 Change the following Logarithmic Equations to Exponential Equations.

  6. 8.4 Logarithmic FunctionsContinued SPECIAL LOGARITHM VALUES Let b be a positive real number such that b ≠ 1. Logarithm of 1  log b1 = 0 because b0= 1 Logarithm of base b  logbb = 1 because b1= b (MEMORIZE THESE VALUES) Ex. 2 Evaluate the expressions without using a calculator.

  7. 8.4 Logarithmic FunctionsContinued • The logarithm with a base 10 is called a COMMONLogarithm. It is denoted by log 10 or simply log. log 10 x = log x (MEMORIZE) • The logarithm with base e is called the NATURAL Logarithm. It is denoted by log e , but it is more often denoted by ln. log e x = ln x (MEMORIZE)

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