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

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Chapter 4.4, Problem 46E
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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.

1 3 [ 2 ln ( x + 3 ) + ln x − ln ( x 2 − 1 ) ]

To determine

To calculate: The reduced form of the expression 13[2ln(x+3)+lnx−ln(x2−1)] using the properties of logarithms.

Explanation

Given Information:

The provided expression is 13[2ln(x+3)+lnx−ln(x2−1)].

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, 13[2ln(x+3)+lnx−ln(x2−1)]

Apply the property of lnxn in the above expression as,

13[2ln(x+3)+lnx−ln(x2−1)]=13[ln(x+3)2+lnx−ln(x2−1)]

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

13[2ln(x+3)+lnx−ln(x2−1)]=13[ln(x+3)2+lnx−ln(x2−1)]=13[ln[x(x+3)

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Representing a Graph by a Vector-Valued Function In Exercises 47-54, represent the plane curve by a vector-valu...

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Solving an Equation In Exercises 69-74, solve the equation accurate to three decimal places. log6(x+1)=2

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RevenueRepeat Exercises 49 after decreasing the prices by 2%. Identify the vector operation used to decrease th...

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01e2xdx= a) 2e2 1 b) `e2 1 c) 12e2 d) 12(e21)

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

Divide the following terms as indicated. 34FS3(3S)

Mathematics For Machine Technology

A population consists of only four individuals identified as A, B, C, and D. Your job is to select a simple ran...

Research Methods for the Behavioral Sciences (MindTap Course List)

Under what circumstances is a proportionate stratified random sample preferred to a simple random sample?

Research Methods for the Behavioral Sciences (MindTap Course List)

Table 1.8 shows a data set containing information for 25 of the shadow stocks tracked by the American Associati...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Consider the following hypothesis test. H0:12=0Ha:120 The following results are for two independent samples tak...

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

Solve each absolute value inequality. Express the solution set in interval notation, and graph it. |3x+5|+19

College Algebra (MindTap Course List)

The paper Predicting Yolk Height, Yolk Width, Albumen Length, Eggshell Weight, Egg Shape Index, Eggshell Thickn...

Introduction To Statistics And Data Analysis

Exercise 5-10 can be done as homework problems or as in-class activities Draw a building in one-point perspecti...

Mathematics: A Practical Odyssey

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