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The first definition of the logarithm was constructed by Napier and popularized through his posthumous pamphlet (Napier 1619). It this pamphlet, Napier sought to reduce the operations of multiplication, division, and root extraction to addition and subtraction. To this end, he defined the "logarithm"L of a number N by N = 10" (1 – 10-7)“, written Nap. log N = L. By repeated subtractions Napier calculated N for L ranging from 1 to 100. Use the binomial theorem to approximate Napier's N .Keep only the first two elements in the expansion. Write your answer in decimal form with 2 decimals after the dot (ex.: A.bc)

The first definition of the logarithm was constructed by Napier and popularized through his posthumous pamphlet (Napier 1619). It this pamphlet, Napier sought to reduce the operations of multiplication, division, and root extraction to addition and subtraction. To this end, he defined the "logarithm"L of a number N by N = 10" (1 – 10-7)“, written Nap. log N = L. By repeated subtractions Napier calculated N for L ranging from 1 to 100. Use the binomial theorem to approximate Napier's N .Keep only the first two elements in the expansion. Write your answer in decimal form with 2 decimals after the dot (ex.: A.bc)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The first definition of the logarithm was constructed by Napier and popularized through his posthumous pamphlet (Napier 1619). It this pamphlet, Napier sought to reduce the operations of multiplication, division, and root extraction to addition and subtraction. To this end, he defined the "logarithm" L of a number N by N = 10° (1 – 10-7)", written Nap. log N = L. By repeated subtractions Napier calculated N for L ranging from 1 to 100 . Use the binomial theorem to approximate Napier's N .Keep only the first two elements in the expansion. Write your answer in decimal form with 2 decimals after the dot (ex.: A.bc)
Transcribed Image Text:The first definition of the logarithm was constructed by Napier and popularized through his posthumous pamphlet (Napier 1619). It this pamphlet, Napier sought to reduce the operations of multiplication, division, and root extraction to addition and subtraction. To this end, he defined the "logarithm" L of a number N by N = 10° (1 – 10-7)", written Nap. log N = L. By repeated subtractions Napier calculated N for L ranging from 1 to 100 . Use the binomial theorem to approximate Napier's N .Keep only the first two elements in the expansion. Write your answer in decimal form with 2 decimals after the dot (ex.: A.bc)
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