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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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In Exercises 14–16, use the properties of logarithms to rewrite the expression as the logarithm of a single quantity. (Assume all variables are positive.)

ln x + 4 ln y 1 2 ln ( z + 4 )

To determine

To calculate: The reduced expression of the expression lnx+4lny12ln(z+4) using the properties of logarithms.

Explanation

Given Information:

The provided expression is lnx+4lny12ln(z+4).

Formula used:

The property of logarithms:

(1) lnxn=nlnx

(2) ln(xy)=lnx+lny

(3) ln(xy)=lnxlny

Where x and y are real numbers greater than 0.

Calculation:

Consider the expression, lnx+4lny12ln(z+4)

Apply the property of lnxn in the above expression as,

lnx+4lny12ln(z+4)=lnx+ln(y4)ln(z+4)12=[lnx

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