Problem

Solve each equation for x. (a) $ \ln (x^2 - 1)…

01:59

Question

Answered step-by-step

Problem 51 Hard Difficulty

Solve each equation for x.

(a) $ e^{7 - 4x} = 6 $
(b) $ \ln (3x - 10) = 2 $

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Mary Wakumoto

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

All right here we have a couple of equations to solve for X. Let's get started. Alright for question A. We have E. To the seven minus four X equal to six. We want to get that X. Out of the expo net. So we can do that by taking natural log of both sides. So natural log of E to the seven minus four X equals natural log of six. Well natural log of E to the seven minus four X is just seven minus four. X. You can look at that by kind of definition of how logs work but you can also notice that Ln of E. Those are composite inverse functions and out pops the argument. So there we have it basically they undo each other and the argument comes out Alright so now let's go ahead and add four X to both sides. Well actually let's subtract seven instead let's go ahead and subtract seven from both sides. And then we can divide both sides by negative four. So L. N S six minus seven over minus four is what X equals. And if I want to go ahead and multiply top and bottom by a negative one then I can rewrite it as seven minus Ln S. Six. All over four. So there we have it, we solve for X. And part A. So let's go ahead and do part B. In this case I want to get the X. Out of my argument of L. N. So I'm gonna do a similar trick. Remember composite inverse functions out pops the argument. So my trick is that I'm gonna take it to both sides. If I take E to both sides, then again these undo each other out potsie argument three x minus 10 equals E squared I can add 10 to both sides, so I'll get E squared plus 10 and finally divide by three. So X. Is E squared plus 10 all over three. Uh So I think we have successfully solved both equations for X. Alright, hopefully that was fun. Have a great day. See you next time.

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

Solve each equation for x. (a) $ \ln (x^2 - 1)…

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

Kayleah Tsai

Samuel Hannah

Calculus 3 Courses

Recommended Videos

Watch More Solved Questions in Chapter 1

Video Transcript

James Stewart

Calculus: Early Transcendentals

Lily An

Heather Zimmers

Kayleah Tsai

Samuel Hannah

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

Calculus: Early Transcendentals

Lily An

Heather Zimmers

Kayleah Tsai

Samuel Hannah

James StewartCalculus: Early Transcendentals

Lily An

Heather Zimmers

Kayleah Tsai

Samuel Hannah

James Stewart

Calculus: Early Transcendentals