   Chapter 4.4, Problem 43E ### 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. 5 ln ( x − 6 ) + 1 2 ln ( 4 x + 1 )

To determine

To calculate: The reduced form of the expression 5ln(x6)+12ln(4x+1) using the properties of logarithms.

Explanation

Given Information:

The provided expression is 5ln(x6)+12ln(4x+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.

Calculation:

Consider the provided expression, 5ln(x6)+12ln(4x+1)

Apply the property of lnxn in the above expression as,

5ln(x6)+12ln(4x+1)=ln(x6)5+ln(4x+1)

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