Problem

Suppose that the graph of $ y = \log_2 x $ is dra…

01:48

Question

Answered step-by-step

Problem 44 Hard Difficulty

Use Formula 10 to graph the given functions on a common screen. How are these graphs related?

$ y = \ln x $ , $ y = \log_{10} x $ , $ y = e^x $ , $ y = 10^x $

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Heather Zimmers

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Johns Hopkins University

Watch More Solved Questions in Chapter 1

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Video Transcript

in this problem. We're using a graphing calculator and we're graphing four grafs on a common screen, and we're seeing how they're related. So we go to y equals and we type them in. We have y equals natural log X Y equals log based 10 of X y equals E to the X and y equals 10 to the X. And for my screen, I decided to go with negative 6 to 10 on the X axis and negative 6 to 10 on the Y axis. You can fiddle around with these numbers and change them to get something that you like. So here, all four graphs at the same time. And if I press trace, I can tell which is which. So the blue one is the natural law graph, and the red one is log based 10. So these have the same basic shape. They both have the same X intercept at one, but the one with a greater base is the lower graph. It's a bit more flat. The black graph is each of the X, and the pink one is 10 to the X, so they have the same basic shape. They're both exponential growth but the one with a greater base grew a lot faster. Tend to the X grows a lot faster than E to the X, and the other thing we want to note is that we do have some inverse is going on here. So the pink one y equals 10th E X is the inverse of the red one, so you can see that pink and red look like reflections across the line Y equals X. In fact, if I graph the line Y equals X, that might help. It's not going to look like it's out of 45 degree angle because my window is kind of skewed. But still, we can see that as a reflection line between the pink and the red. And also the blue and the black are in verses. The blue one was the natural log function, and the black is the E to the X function, and they're also reflections across the line Y equals X

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem

Suppose that the graph of $ y = \log_2 x $ is dra…

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 3 Educators

Lily An

Heather Zimmers

Kristen Karbon

Joseph Lentino

Calculus 3 Courses

Recommended Videos

Watch More Solved Questions in Chapter 1

Video Transcript

James Stewart

Calculus: Early Transcendentals

Lily An

Heather Zimmers

Kristen Karbon

Joseph Lentino

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Lily An

Heather Zimmers

Kristen Karbon

Joseph Lentino

James StewartCalculus: Early Transcendentals

Lily An

Heather Zimmers

Kristen Karbon

Joseph Lentino

James Stewart

Calculus: Early Transcendentals