   Chapter 4.4, Problem 37E ### 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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# Using Properties of Logarithms In Exercises 37 and 38, use the properties of logarithms and the fact that In 2  ≈  0 .6931 and ln 3  ≈  1 .0986 to approximate the logarithm. Then use a calculator to confirm your approximation.(a) ln 6 (b) ln 2 3 (c) ln 81 (d) ln 3

(a)

To determine

To calculate: The value of the expression ln(6) by using the properties of logarithm such that ln20.6931 and ln31.0986. Also, check the value by using a calculator.

Explanation

Given Information:

The provided expression is ln(6) such that ln20.6931 and ln31.0986.

Formula used:

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, ln(6)

Rewrite the expression as,

ln(6)=ln(23)

Now, apply the property ln(xy)=lnx+lny as,

ln(6)=ln(23)=ln2+ln3

Now, substitute the values ln20

(b)

To determine

To calculate: The value of the expression ln(23) by using the properties of logarithm such that ln20.6931 and ln31.0986. Also, check the value by using a calculator.

(c)

To determine

To calculate: The value of the expression ln(81) by using the properties of logarithm such that ln20.6931 and ln31.0986. Also, check the value by using a calculator.

(d)

To determine

To calculate: The value of the expression ln(3) by using the properties of logarithm such that ln20.6931 and ln31.0986. Also, check the value by using a calculator.

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