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8.5 Natural Logarithms

8.5 Natural Logarithms. ©2001 by R. Villar All Rights Reserved. Natural Logarithms. Natural Logarithm: if x is a positive real number, then the natural logarithm of x is denoted by log e x or ln x A function given by f(x) = a + ln bx is called a natural logarithm function.

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8.5 Natural Logarithms

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  1. 8.5 Natural Logarithms ©2001 by R. Villar All Rights Reserved

  2. Natural Logarithms Natural Logarithm:if x is a positive real number, then the natural logarithm of x is denoted by loge x or ln x A function given by f(x) = a + lnbx is called a natural logarithm function. Example: Use your calculator to find ln 3 Your scientific calculator has a natural logarithm key on it. ln 3 = 1.0986 Let’s look at the graph of a natural logarithm function...

  3. Ex. Graph f(x) = 3 – ln (x – 1) x f(x)

  4. Ex. Graph f(x) = 3 – ln (x – 1) 1.25 x f(x)

  5. Ex. Graph f(x) = 3 – ln (x – 1) 1.25 1.5 2 3 4 5 6 x f(x)

  6. Ex. Graph f(x) = 3 – ln (x – 1) 1.25 1.5 2 3 4 5 6 4.38 x f(x)

  7. Ex. Graph f(x) = 3 – ln (x – 1) 1.25 1.5 2 3 4 5 6 4.38 3.69 3 2.31 1.90 1.611.39 x f(x)

  8. Ex. Graph f(x) = 3 – ln (x – 1) 1.25 1.5 2 3 4 5 6 4.38 3.69 3 2.31 1.90 1.611.39 x f(x)

  9. Ex. Graph f(x) = 3 – ln (x – 1) 1.25 1.5 2 3 4 5 6 4.38 3.69 3 2.31 1.90 1.611.39 The line x = 1 is the vertical asymptote of The function. x f(x)

  10. Natural logarithms can be condensed/expanded using the properties of logarithms: Condense the expressions:a. ln 18 – ln 3b. 3ln x + ln y c. = ln 6 = ln x3y =ln 41/2 + 2 ln 3 =ln 2+ ln 32 = ln 2 + ln 9 = ln 18

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