Chapter 13 Exponential Functions and Logarithmic Functions.

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Presentation transcript:

Chapter 13 Exponential Functions and Logarithmic Functions

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions Laws of Integral Indices

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions Positive n th Root

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions Rational Indices Let

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions Exponential Functions If a function is defined as y  ka x for constants a and k where a  0, a  1 and k  0, then the function is called an exponential function.

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions Graphs of Exponential Functions

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions Symmetry of Graphs of Exponential Functions

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions John Napier John Napier ( ), a Scottish mathematician, invented logarithm to handle lengthy computation such as multiplication, division and calculation involving indices.

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions Common Logarithms

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions Graph of a Common Logarithmic Function For the function y  log x, x must be a positive number. Its graph is always sloping upwards from the left to right.

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions Properties of Common Logarithms

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions Applications of Common Logarithms

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions Solving Exponential Equations Solve 3 x  5. (corr. to 2 d.p.) Solution:

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions Transforming Exponential Graphs into Linear Graphs log y  log [3(2 x )]  log y  log 3  xlog 2

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions The Decibel Scale

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions The Decibel Scale

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions The Richter Scale

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions The Richter Scale

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions Definition of logarithms to base a

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions Graphs of Logarithmic Functions y  log a x (where a  0, a  1 and x  0)

2005 Chung Tai Educational Press © Chapter Examples Quit Chapter 13 Exponential Functions and Logarithmic Functions Symmetry of Graphs of Exponential and Logarithmic Functions

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