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Logarithms and Their Properties Lesson 4.1. Recall the Exponential Function General form  Given the exponent what is the resulting y-value? Now we look.

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Presentation on theme: "Logarithms and Their Properties Lesson 4.1. Recall the Exponential Function General form  Given the exponent what is the resulting y-value? Now we look."— Presentation transcript:

1 Logarithms and Their Properties Lesson 4.1

2 Recall the Exponential Function General form  Given the exponent what is the resulting y-value? Now we look at the inverse of this function  Now we will ask, given the result, what exponent is needed to achieve it?

3 A New Function Consider the exponential function y = 10 x Based on that function, declare a new function x = log 10 y You should be able to see that these are inverse functions In general The log of a number is an exponent

4 The Log Function Try These log 3 9 = ?log 2 32 = ? log 0.01 = ? Note: if no base specified, default is base of 10

5 Properties of Logarithms Note box on page 154 of text Most used properties

6 Natural Logarithms We have used base of 10 for logs Another commonly used base for logs is e  e is an irrational number (as is ) e has other interesting properties  Later to be discovered in calculus Use ln button on your calculator

7 Properties of the Natural Logarithm Recall that y = ln x  x = e y Note that  ln 1 = 0 and ln e = 1  ln (e x ) = x (for all x)  e ln x = x (for x > 0) As with other based logarithms

8 Use Properties for Solving Exponential Equations Given Take log of both sides Use exponent property Solve for what was the exponent Note this is not the same as log 1.04 – log 3

9 Misconceptions log (a+b) NOT the same as log a + log b log (a-b) NOT the same as log a – log b log (a * b) NOT same as (log a)(log b) log (a/b) NOT same as (log a)/(log b) log (1/a) NOT same as 1/(log a)

10 Assignment Lesson 4.1 Page 157 Exercises 1 – 51 odd


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