   Chapter 4.4, Problem 41E ### 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. 3 ln x + 2 ln y − 4 ln z

To determine

To calculate: The reduced form of the expression 3lnx+2lny4lnz using the properties of logarithms.

Explanation

Given Information:

The provided expression is 3lnx+2lny4lnz.

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, 3lnx+2lny4lnz

Apply the property of lnxn in the above expression as,

3lnx+2lny4lnz=ln(x3)+ln(y2)ln(z4)=[ln(x3)+ln(y2

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