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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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Using Properties of Logarithms In Exercises 37 and 38, use the properties of logarithms and the fact that In  0 .6931 and ln 3   1 .0986 to approximate the logarithm. Then use a calculator to confirm your approximation.

(a) ln 0.25 (b) ln 24 (c) ln 12 3

(d) ln 1 12

(a)

To determine

To calculate: The value of the expression ln(0.25) 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(0.25) such that ln20.6931 and ln31.0986.

Formula used:

The property of logarithms for the expression ln(xy) is ln(xy)=lnxlny where x and y are real numbers greater than 0.

The property of logarithms for the expression lnxn is lnxn=nlnx where x and y are real numbers greater than 0.

Calculation:

Consider the provided expression, ln(0.25)

Rewrite the expression as,

ln(0.25)=ln(25100)=ln(14)

Now, apply the property ln(xy)=lnxlny as,

ln(0.25)=ln(14)=ln1ln4=ln1ln(2)2

Apply the property lnxn=nlnx as,

ln(0

(b)

To determine

To calculate: The value of the expression ln(24) 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(123) 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(172) 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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