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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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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.

7 ln ( 5 x + 8 ) 3 2 ln ( x 9 )

To determine

To calculate: The reduced form of the expression 7ln(5x+8)32ln(x9) using the properties of logarithms.

Explanation

Given Information:

The provided expression is 7ln(5x+8)32ln(x9).

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)=lnxlny where x and y are real numbers greater than 0.

Calculation:

Consider the provided expression, 7ln(5x+8)32ln(x9)

Apply the property of lnxn in the above expression as,

7ln(5x+8)32ln(x9)=ln(5x+8)7ln(x9)32

Now, apply the property of ln(xy) as,

7ln(5x+8)

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