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

(a) What is the natural logarithm? (b) What is t…

01:16

Question

Answered step-by-step

Problem 33 Hard Difficulty

(a) How is the logarithmic function $ y = \log_b x $ defined?
(b) What is the domain of this function?
(c) What is the range of this function?
(d) Sketch the general shape of the graph of the function $ y = \log_b x $ if $ b > 1 $.


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

02:31

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

Heather Zimmers

Oregon State University

Kayleah Tsai

Harvey Mudd 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

01:35

(a) How is the logarithmic…

02:07

(2) How is the logarithmic…

02:33

How Is the logarithmic fun…

01:08

Given the logarithmic func…

01:00

Given the logarithmic func…

02:43

(a) Write an equation that…

02:22

(a) Write an equation that…

01:39

a. Graph $Y_{1}=\log (x-1)…

01:19

For $b>0$ with $b \neq …

01:50

a. Graph $Y_{1}=\log x^{2}…

07:15

graph each function and sp…

00:56

What are the domain and ra…

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 looking at some of the most important features of the basic log rhythmic function Y equals log base be of X. And did you know that this came from trying to find the inverse of y equals B to the X power? So this is an exponential function y equals B to the X. If we found its inverse, it would be X equals B to the why so the definition of the log rhythmic function why equals log Base P of X is that it is equivalent to X equals B to the why now the base has to be a number that's greater than zero, and all their basic rules for exponential functions apply. All right, So what is the domain and what is the range of this log rhythmic function? Well, knowing that it's the inverse of the exponential function, how about if we start by finding the domain and range of the exponential function, and then we switch them to get the domain a range of the log rhythmic function. So we know the exponential function, particularly if the base is greater than one is going to look like this. It's domain is all real numbers and its range is. Why is greater than zero if we write those in interval notation we have the domain is negative. Infinity to infinity on the range is zero to infinity. So for the log rhythmic function, we're going to switch those and the domain will be what the range waas for the exponential and vice versa. So the domain will be zero to infinity. On the range will be negative. Infinity to infinity. Now what does the graph look like? Particularly if the base is greater than one. So it's going to look like the inverse of the exponential curve, which means the reflection of that curve across the line y equals X, and that's going to be something like this.

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
153
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
68
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

Heather Zimmers

Oregon State University

Kayleah Tsai

Harvey Mudd 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

01:35

(a) How is the logarithmic function y = logb(x) defined? It is defined as the i…

02:07

(2) How is the logarithmic function logb defined? It is defined as the inverse …

02:33

How Is the logarithmic function logb(x) defined? It is defined as the inverse o…

01:08

Given the logarithmic function y loga x: (a) What is the domain of the function…

01:00

Given the logarithmic function y=logax (a) What is the domain of the function? …

02:43

(a) Write an equation that defines the exponential function with base $ b > 0 $…

02:22

(a) Write an equation that defines the exponential function with base $ b > 0 $…

01:39

a. Graph $Y_{1}=\log (x-1)^{2}$ and state its domain. b. Graph $Y_{2}=2 \log (x…

01:19

For $b>0$ with $b \neq 1,$ what are the domain and range of $f(x)=\log _{b} x$ …

01:50

a. Graph $Y_{1}=\log x^{2}$ and state its domain. b. Graph $Y_{2}=2 \log x$ and…

07:15

graph each function and specify the domain, range, intercept(s), and asymptote.…

00:56

What are the domain and range of the function defined by $$ y=\log (x-1)-1 ? $$
Additional Mathematics Questions

02:31

Below is a payoff table involving three states of nature and
three decisi…

04:24

Boxes are labeled as containing 400 g of cereal. The
machine filling the …

01:04

Given an actual demand of 61, forecast of 55, and an alpha
factor of .3, …

05:35


A:Assume that when adults with smartphones are
randomly selected,56%…

01:48

A rope is being wound around a drum with a radius of 12ft.How
much rope i…

03:25

Find a formula for the exponential function which satisfies the
given con…

00:59

Carry the answer to three decimal places.
What is the total thickness of …

00:47

Carry the answer to two decimal places. What is the cost of
1,250 feet of…

01:28

The graph of y = –2 sin (x – 2) + 1 has amplitude of:
Select one:
a. 0…

02:18

Given a population in which p = 0.6 and a random sample from
this populat…

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