Problem

Compare the functions $ f(x) = x^{0.1} $ and $ g(…

02:47

Problem 45 Hard Difficulty

Suppose that the graph of $ y = \log_2 x $ is drawn on a coordinate grid where the unit of measurement is an inch. How many miles to the right of the origin do we have to move before the height of the curve reaches 3 ft?

Answer

1084587.7 $\mathrm{mi}$

More Answers

02:59

Jeffrey P.

Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

Discussion

You must be signed in to discuss.

Top Calculus 3 Educators

Catherine R.

Missouri State University

Caleb E.

Baylor University

Samuel H.

University of Nottingham

Michael J.

Idaho State 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

for this problem. We have the graph of y equals log based two of X, and I've made a rough sketch of it. We know it goes through the X axis at the 20.10 and we're interested in finding out what its X corn it is. When the Y coordinate is three feet, every unit is one inch, so three feet will be 36 inches. So what is the X coordinate when the Y coordinate is 36 inches? How far out would we have to go? Well, what we can do is take our function log based two of X and set it equal to 36. Substitute 36 in for why and when we saw that we get X equals two to the 36th Power. Now, if you put that in your calculator, you get a very, very large number. It's it changes it to scientific notation. I can only write part of its 6.87 times 10 to the 10th inches. Now let's convert that into miles, so it'll be easier to manage. So to convert it into feet, we would divide it by 12. Now we have feet and to convert it to Miles. We would divide that by 5280 because there are 5280 feet in a mile, and once we divide by both of those numbers, we end up with one million 84,000 587 0.7 miles. That's how far you would have to go to reach a height of three feet on this graph. That is pretty extreme. That shows us just how slowly this graph is growing.

Heather Z.

Oregon State University

Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

Top Calculus 3 Educators

Catherine R.

Missouri State University

Caleb E.

Baylor University

Samuel H.

University of Nottingham

Michael J.

Idaho State University