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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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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)=lnx−lny 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)]−

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Sect-4.1 P-1CPSect-4.1 P-2CPSect-4.1 P-3CPSect-4.1 P-4CPSect-4.1 P-5CPSect-4.1 P-1SWUSect-4.1 P-2SWUSect-4.1 P-3SWUSect-4.1 P-4SWUSect-4.1 P-5SWU
Sect-4.1 P-6SWUSect-4.1 P-7SWUSect-4.1 P-8SWUSect-4.1 P-9SWUSect-4.1 P-10SWUSect-4.1 P-11SWUSect-4.1 P-12SWUSect-4.1 P-13SWUSect-4.1 P-14SWUSect-4.1 P-15SWUSect-4.1 P-16SWUSect-4.1 P-17SWUSect-4.1 P-18SWUSect-4.1 P-1ESect-4.1 P-2ESect-4.1 P-3ESect-4.1 P-4ESect-4.1 P-5ESect-4.1 P-6ESect-4.1 P-7ESect-4.1 P-8ESect-4.1 P-9ESect-4.1 P-10ESect-4.1 P-11ESect-4.1 P-12ESect-4.1 P-13ESect-4.1 P-14ESect-4.1 P-15ESect-4.1 P-16ESect-4.1 P-17ESect-4.1 P-18ESect-4.1 P-19ESect-4.1 P-20ESect-4.1 P-21ESect-4.1 P-22ESect-4.1 P-23ESect-4.1 P-24ESect-4.1 P-25ESect-4.1 P-26ESect-4.1 P-27ESect-4.2 P-1CPSect-4.2 P-2CPSect-4.2 P-3CPSect-4.2 P-4CPSect-4.2 P-5CPSect-4.2 P-1SWUSect-4.2 P-2SWUSect-4.2 P-3SWUSect-4.2 P-4SWUSect-4.2 P-5SWUSect-4.2 P-6SWUSect-4.2 P-7SWUSect-4.2 P-8SWUSect-4.2 P-9SWUSect-4.2 P-10SWUSect-4.2 P-11SWUSect-4.2 P-12SWUSect-4.2 P-1ESect-4.2 P-2ESect-4.2 P-3ESect-4.2 P-4ESect-4.2 P-5ESect-4.2 P-6ESect-4.2 P-7ESect-4.2 P-8ESect-4.2 P-9ESect-4.2 P-10ESect-4.2 P-11ESect-4.2 P-12ESect-4.2 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In Exercises 15 to 20, use the sine, cosine, or tangent ratio to find the lengths of the indicated sides to the...

Elementary Geometry for College Students

Write as an iterated integral, where D is shown at the right.

Study Guide for Stewart's Multivariable Calculus, 8th

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In Exercises 1928, find the conservative vector field for the potential function by finding its gradient. g(x,y...

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Writing Exercises 35 and 36, use a graphing utility to graph the polar equations and approximate the points of ...

Calculus (MindTap Course List)

Using Properties of Exponents In Exercises 107-110, find the exact value of the expression. 51/ln5

Calculus

In exercise 1, the following estimated regression equation based on 10 observations was presented. = 29.1270 +...

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The following dimensions are given with bilateral tolerances. For each value determine the maximum dimension (m...

Mathematics For Machine Technology

Suppose that you were asked to help design a survey of adult city residents in order to estimate the proportion...

Introduction To Statistics And Data Analysis

Describe the general purpose of an experimental research study, differentiate experiments from other types of r...

Research Methods for the Behavioral Sciences (MindTap Course List)

Suppose that we have two events, A and B, with P(A) = .50, P(B) = .60, and P(A B) = .40. a. Find P(A B). b. F...

Statistics for Business & Economics, Revised (MindTap Course List)

Let fx=x2-7and gx=x. Find each function and its domain. f+g

College Algebra (MindTap Course List)

Finding the area of a Sierpinski carpet. See Exercise 2 in Section 8.9 for a description of this fractal. By ar...

Mathematics: A Practical Odyssey

Describe some of the problems that can arise when the participants in one treatment condition of a between-subj...

Research Methods for the Behavioral Sciences (MindTap Course List)

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