Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Solve each inequality for x. (a) $ 1< e^{3x - …
02:06

Question

Answered step-by-step

Problem 55 Hard Difficulty

Solve each inequality for x.

(a) $ \ln x < 0 $
(b) $ e^x > 5 $

Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Heather Zimmers
Numerade Educator

Like

Report

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

More Answers

00:44

Jeffrey Payo

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus 3
Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

Related Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Discussion

You must be signed in to discuss.
Top Calculus 3 Educators
Lily An

Johns Hopkins University

Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Joseph Lentino

Boston College

Calculus 3 Courses

Lectures

Video Thumbnail

04:31
Multivariate Functions - Intro

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.
Video Thumbnail

12:15
Partial Derivatives - Overview

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.
Join Course
Recommended Videos

08:04

Solve each inequality for …

01:02

Solve each inequality for …

02:06

Solve each inequality for …

01:03

Solve the inequality for $…

00:43

$55-56$ Solve each inequal…

01:04

$51-52$ Solve each inequal…

00:41

Solve each inequality.
…

00:55

Solve each equation or ine…

02:47

Solve each inequality.
…

01:20

Solve each inequality.
…

01:03

$39-40$ Solve each inequal…

01:10

$51-52$ Solve each inequal…

01:09

Solve the inequality analy…

01:07

Solve the inequality for $…

01:26

Solve the inequality.
$…

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

I'm going to solve both of these inequalities algebraic Lee and then confirmed them graphically. So first of all, with natural log of X is less than zero. I'm going to use a process called exponentially ating, which means that each side of the equation or each side of the inequality will be an exponents on the same base. And I'm going to use based E. So we hav e raised to the left side of the inequality is less than e raised to the right side of the inequality. And we should know, based on inverse functions that e to the natural log of X simplifies to just be X, and each of zero is one, so we have X is less than one. There's one other thing we need to consider, though. Remember the domain of along with Mick Function X has to be greater than zero. So we do have X is less than one, and we have X is greater than zero. When you combine those together, you get zero is less than X is less than one now. Graphically, if you think about what the natural log of X function looks like, it looks like this with the next intercept at one. Where is it greater than zero Down here. We're sorry. Less than zero down here that that's where the Y values are. Less than zero. And that was between X equals zero and X equals one. Okay, now let's do something similar to the other inequality. And I'm going to take the natural log of both sides. So we have natural log of e to the X is greater than natural law. Go five because of inverse functions. Natural log of each of the X simplifies to just be x so x is greater than natural log five.

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.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
162
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
70
Hosted by: Alonso M
See More

Related Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Top Calculus 3 Educators
Lily An

Johns Hopkins University

Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Joseph Lentino

Boston College

Calculus 3 Courses

Lectures

Video Thumbnail

04:31
Multivariate Functions - Intro

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.
Video Thumbnail

12:15
Partial Derivatives - Overview

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.
Join Course
Recommended Videos

08:04

Solve each inequality for x. $$(a)1< e^{3 x-1}<2 \quad \text { (b) } 1-2 \ln…

01:02

Solve each inequality for $x .$ $$ \text { (a) }1<e^{3 x-1}<2 \quad \text { (…

02:06

Solve each inequality for x. (a) $ 1< e^{3x - 1} < 2 $ (b) $ 1 - 2 \ln x < …

01:03

Solve the inequality for $x.$ $$e^{x}>5$$

00:43

$55-56$ Solve each inequality for $x$ (a) $\ln x<0 \quad$ (b) $e^{x}>5$

01:04

$51-52$ Solve each inequality for $x$ (a) $e^{x}<10 \quad$ (b) $\ln x>-1$

00:41

Solve each inequality. $$3+\ln x>e^{x}$$

00:55

Solve each equation or inequality. $e^{2 x}>5$

02:47

Solve each inequality. $$\left(e^{x}-2\right)\left(e^{x}-3\right)<2 e^{x}$$

01:20

Solve each inequality. $$5 \log x+2>0$$

01:03

$39-40$ Solve each inequality for $x$ $$\text { (a) }\ln x<0 \quad \text { (b)…

01:10

$51-52$ Solve each inequality for $x$ (a) $2<\ln x<9 \quad$ (b) $e^{2-3 x}>4$

01:09

Solve the inequality analytically. $$ x \ln (x)-x>0 $$

01:07

Solve the inequality for $x.$ $$-2<\ln x<0$$

01:26

Solve the inequality. $$x^{2} e^{x}-2 e^{x}<0$$
Additional Mathematics Questions

01:06

Toe median annual income In a certain town is $54,000, A sample median of 56…

01:19

A recent poll found that 30% of those surveyed are worried about aggressive …

02:04

The lengths of human pregnancies are normally distributed with a mean of 4 =…

04:50

Tak
Tank D
Figure 1: 2 Tank System
You have two tanks, Tank A, whic…

04:39

Age of first heart attack The horizontal axis is age. The vertical axis Is f…

01:58

Question 19
Mint Wnet
mtu !
Fla qucxion
100 pcoplc arc tested fo…

01:00

Imagine you survey your friends to find the kind movie they like best; the r…

03:07

new drug [s being proposed forthe treatmentof migraine hcadachex Unfortunatc…

04:49

Question # 4 Given a normally distributed population with a mean of 100 and …

04:07

A sociologist randomly selects single adults for different groups of three, …

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started