   Chapter 4.4, Problem 45E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
5 views

# Condensing Logarithmic Expressions In Exercises 39–46, use the properties of logarithms to rewrite the expression as the logarithm of a single quantity. (Assume all variables are positive.) See Example 4. 2 3 [ ln   x + ln ( x + 5 ) − 4 ln ( x 2 + 4 ) ]

To determine

To calculate: The reduced form of the expression 23[lnx+ln(x+5)4ln(x2+4)] using the properties of logarithms.

Explanation

Given Information:

The provided expression is 23[lnx+ln(x+5)4ln(x2+4)].

Formula used:

The property of logarithms for the expression lnxn is lnxn=nlnx where x and y are real numbers greater than 0.

The property of logarithms for the expression ln(xy) is ln(xy)=lnx+lny where x and y are real numbers greater than 0.

The property of logarithms for the expression ln(xy) is ln(xy)=lnxlny where x and y are real numbers greater than 0.

Calculation:

Consider the provided expression, 23[lnx+ln(x+5)4ln(x2+4)]

Apply the property of lnxn in the above expression as,

23[lnx+ln(x+5)4ln(x2+4)]=23[lnx+ln(x+5)ln(x2+4)4]

Now, apply the property of ln(xy) as,

23[lnx+ln(x+5)4ln(x2+4)]=23[lnx+ln(x+5)ln(x2+4)4]=23[ln[x(x+5)]ln(x2+4)4]

Then, apply the property of ln(xy) as,

23[lnx+ln(x+5)4ln(x2+4)]=23[ln[x(x+5)]

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find the limit. limxln(sinx)

Single Variable Calculus: Early Transcendentals, Volume I

#### What is the value of (X + 1) for the following scores: 0, 1, 4, 2? a. 8 b. 9 c. 11 d. 16

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### Simplify each of the following so that only positive exponents remain.

Mathematical Applications for the Management, Life, and Social Sciences

#### ∫x−4dx = −4x−5 + C

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 