
How many numbers between 1 and 20 can be approximated using the given values of logarithms?

Answer to Problem 119E
Apart from 2, 3 and 5, nine more numbers can be approximated between 1 and 20 using the given values of logarithms.
Explanation of Solution
Given:
Three logarithms: ln2=0.6931,ln3=1.0986,ln5=1.6094 .
Calculation:
The following numbers can be approximated using the given three logarithms:
2,3,4,5,6,8,9,10,12,15,16,18
Below are the calculations for each one of these numbers:
ln2=0.6931(Given)ln3=1.0986(Given)ln4=ln22=2ln2=2×0.6931=1.3862ln5=1.6094(Given)ln6=ln(2×3)=ln2+ln3=0.6931+1.0986=1.7917ln8=ln23=3ln2=3×0.6931=2.0793ln9=ln32=2ln3=2×1.0986=2.1972ln10=ln(2×5)=ln2+ln5=0.6931+1.6094=2.3025ln12=ln(22×3)=2ln2+ln3=2×0.6931+1.0986=2.4848ln15=ln(3×5)=ln3+ln5=1.0986+1.6094=2.708ln16=ln24=4ln2=4×0.6931=2.7724ln18=ln(2×32)=ln2+2ln3=0.6931+2×1.0986=2.8903
Chapter 3 Solutions
Precalculus with Limits: A Graphing Approach
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