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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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Expanding Logarithmic Expressions In Exercises 57-62, use the properties of logarithms to rewrite the expression as a sum, difference, or multiple of logarithms. (Assume all variables are positive.)

ln x 2 ( x 1 )

To determine

To calculate: The value of the expression lnx2(x1) using the properties of logarithms.

Explanation

Given Information:

The provided expression is lnx2(x1).

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 expression, lnx2(x1)

Rewrite the expression as,

lnx2(x1)=ln[x2(x1)]12

Apply the property of lnxn in the above expression as,

ln[x2(x1)]12=12ln[x2(x1)]

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