Download presentation

Presentation is loading. Please wait.

Published byErnest Pierce Modified over 8 years ago

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 log e x or ln x A function given by f(x) = a + ln bx 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) x f(x) 1.25

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

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

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

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

9
Ex. Graph f(x) = 3 – ln (x – 1) x f(x) 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.

10
Condense the expressions: a. ln 18 – ln 3 b.3ln x + ln y c. = ln 6 = ln x 3 y = ln 4 1/2 + 2 ln 3 = ln 2 + ln 3 2 = ln 2 + ln 9 = ln 18 Natural logarithms can be condensed/expanded using the properties of logarithms:

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google