   Chapter 4.4, Problem 46E ### 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
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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)+lnxln(x21)] using the properties of logarithms.

Explanation

Given Information:

The provided expression is 13[2ln(x+3)+lnxln(x21)].

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, 13[2ln(x+3)+lnxln(x21)]

Apply the property of lnxn in the above expression as,

13[2ln(x+3)+lnxln(x21)]=13[ln(x+3)2+lnxln(x21)]

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

13[2ln(x+3)+lnxln(x21)]=13[ln(x+3)2+lnxln(x21)]=13[ln[x(x+3)

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