/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 93 Explain how to find the domain o... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 93

Explain how to find the domain of a logarithmic function.

Short Answer

Expert verified
The domain of a logarithmic function is all real numbers greater than zero.

Step by step solution

01

Understand the Function

First, one must understand what a logarithmic function is. It is the inverse of an exponential function. The notation is \(y = \log_{b}(x)\), where b is the base of the logarithm.
02

Identify the Constraints

The logarithmic functions are undefined for values of x that are less than or equal to zero. This is because logarithms represent the exponent to which the base must be raised to get the argument. There is no exponent that you can raise a positive number to that will result in zero or a negative number.
03

Set the Domain

Given the constraints, the domain of a logarithmic function is all real numbers greater than zero. This can be expressed in interval notation as \(x > 0\) or in set notation as \{x 鈭� 鈩�: x > 0\}.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log \sqrt{100 x} $$

Describe the product rule for logarithms and give an example.

In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log \left(\frac{x}{100}\right) $$

You overhear a student talking about a property of logarithms in which division becomes subtraction. Explain what the student means by this.

In Exercises \(71-78,\) use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. $$ \log _{16} 57,2 $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.