Math 71B 9.3 – Logarithmic Functions 1. One-to-one functions have inverses. Let’s define the inverse of the exponential function. 2.

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Presentation transcript:

Math 71B 9.3 – Logarithmic Functions 1

One-to-one functions have inverses. Let’s define the inverse of the exponential function. 2

3 Logarithmic Function

4 logarithmic function

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Ex 1. Write each equation in the other form. 6 Exponential FormLogarithmic Form

Ex 1. Write each equation in the other form. 7 Exponential FormLogarithmic Form

Ex 1. Write each equation in the other form. 8 Exponential FormLogarithmic Form

Ex 1. Write each equation in the other form. 9 Exponential FormLogarithmic Form

Ex 1. Write each equation in the other form. 10 Exponential FormLogarithmic Form

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20 Graph of Logarithmic Function

21 Graph of Logarithmic Function

22 Graph of Logarithmic Function

23 Graph of Logarithmic Function

24 Graph of Logarithmic Function

25 Graph of Logarithmic Function

26 Graph of Logarithmic Function What is the vertical asymptote? _________ What is the domain? _________ What is the range? _________

27 Graph of Logarithmic Function What is the vertical asymptote? _________ What is the domain? _________ What is the range? _________

28 Graph of Logarithmic Function What is the vertical asymptote? _________ What is the domain? _________ What is the range? _________

29 Graph of Logarithmic Function What is the vertical asymptote? _________ What is the domain? _________ What is the range? _________

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40 common natural