1. History of Logarithms
Logarithms were invented independently by John Napier, a Scotsman, and by Joost
Burgi, a Swiss. Napier's logarithms were published in 1614; Burgi's logarithms were
published in 1620. The objective of both men was to simplify mathematical
calculations.
It can’t be said too often: a logarithm is nothing more than an exponent.
The basic concept of logarithms can be expressed as a shortcut…
Multiplication is a shortcut for Addition: 3 x 5 means 5 + 5 + 5
Exponents are a shortcut for Multiplication: 4^3 means 4 x 4 x 4
Logarithms are a shortcut for Exponents: 10^2 = 100.
Before pocket calculators you needed logs to compute most powers and roots with
fair accuracy; even multiplying and dividing most numbers were easier with logs.
The invention of logs in the early 1600s fueled the scientific revolution. Back then
scientists, astronomers especially, used to spend huge amounts of time crunching
numbers on paper. By cutting the time they spent doing arithmetic, logarithms
effectively gave them a longer productive life.
Today, logs are no longer used in routine number crunching. But there are still good
reasons for studying them. Why do we use logarithms, anyway?
• To model many natural processes, particularly in living systems. We perceive
loudness of sound as the logarithm of the actual sound intensity, and dB (decibels) are
a logarithmic scale. We also perceive brightness of light as the logarithm of the actual
light energy, and star magnitudes are measured on a logarithmic scale.
• To measure the pH or acidity of a chemical solution. The pH is the negative
logarithm of the concentration of free hydrogen ions.
• To measure earthquake intensity on the Richter scale.
John Napier
John Napier of Merchiston (1550 – 4
April 1617) – also signed as Neper,
Nepair – named Marvellous Merchiston,
was a Scottish mathematician, physicist,
astronomer and astrologer, and also the 8th
Liard of Merchistoun. John Napier is
most renowned as the discoverer of the
logarithm. Napier also made common the
use of the decimal point in arithmetic and

2. mathematics. Napier's birthplace, the Merchiston Tower in Edinburgh, Scotland, is
now part of the facilities of Edinburgh Napier University. After his death from the
effects of gout, Napier's remains were buried in St Cuthbert's Church, Edinburgh.
His work, Mirifici Logarithmorum Canonis Descriptio (1614) contained fifty-seven
pages of explanatory matter and ninety pages of tables of numbers related to natural
logarithms.
Napier made further contributions. He improved decimal notation. Arab lattice
multiplication used by Fibonacci, was made more convenient by his introduction of
Napier's bones, a multiplication tool using a set of numbered rods.
List of works
• (1593) A Plaine Discovery of the Whole Revelation of St. John
• (1614) Mirifici logarithmorum canonis descriptio (Edward Wright's English translation was
published in 1616).
• (1617)Rabodologiae seu Numerationes per Virgulas libri duo (published posthumously)
• (1619)Mirifici logarithmorum canonis constructio (written before the Descriptio, but
published posthumously by his son Robert)
Questions:
1. Tell the names of the two men that invented logarithms.
2. What was their objective.
3. Why logarithms fueled the scientific revolution?
4. Write two uses of logarithms today.
5. How old was Napier when he died? What caused his death?
6. Where was he born?
7. Write two other contributions of Napier to mathematics.
8. What book did he published in 16th century?
9. What are “Napier's bones”?
10.Look in the text for the words that fit to the following definitions:
– Moderately large; ample:___________________
– In or during the first part of a period of time, a course of action, a series of
events, etc.:__________
– Extraordinarily large in bulk, quantity, or extent: _______________
– A method, procedure, policy, etc., that reduces the time or energy needed to
accomplish something:_____________
– Additional; more: _____________
– Arising, occurring, or continuing after one's death: _____________
– A stick, wand, staff, or the like, of wood, metal, or other material:___________