   Chapter 4.4, Problem 35E ### 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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# Expanding Logarithmic Expressions In Exercises 27–36, use the properties of logarithms to rewrite the expression as a sum, difference, or multiple of logarithms. (Assume all variables are positive.) See Example 3. ln   3 x ( x + 1 ) ( 2 x + 1 ) 2

To determine

To calculate: The value of the expression ln3x(x+1)(2x+1)2 with the help of properties of logarithms.

Explanation

Given Information:

The provided expression is ln3x(x+1)(2x+1)2.

Formula used:

The power rule for any positive number M is such that, lnMk=klnM, where k is any real number and a is the base of logarithm.

The quotient rule for any positive numbers M and N, lnMN=lnMlnN.

The product rule for any positive numbers M and N, ln(MN)=lnM+lnN.

Calculation:

Consider the expression,

ln3x(x+1)(2x+1)2

Use the quotient rule of logarithms,

ln3x(x+1)(2x+1)2=ln[3x(x+1)]ln(

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