# Logarithm

In the 1500s and early 1600s, although science, engineering, and medicine were flourishing, many people did not understand multiplication tables. Mathematicians, astronomers, navigators, and scientists were forced to spend a lot of time performing calculations, so that little time was left to work on experiments and new discoveries. Finally, around 1594 Scottish mathematician John Napier (1550–1617) produced a table of logarithmic, or proportionate, numbers.

## How logarithms work

In the commonly known base 10 system, computations that involve very large numbers can become difficult, if not incomprehensible. Napier realized numbers could be more easily expressed in terms of powers. Thus 100 is equal to 10 multiplied by 10, written as 10 2 . This is read as "10 squared" and means "10 to the power two."

To perform multiplication, numbers are converted into logarithms, the exponents added together, and the result converted back into base 10. Likewise, to perform division, two logarithmic exponents are subtracted, and the result converted back to base 10.

This innovative way of multiplying and dividing large numbers was a milestone event for mathematicians of the day. Napier's tables were published in 1614 and were put into use immediately, becoming an essential part of the mathematical, scientific, and navigational processes.

Logarithmic tables remained popular throughout the next several centuries and were used as the basis for many mechanical calculating devices. Relieved from much of their mental drudgery, scientists and mathematicians enjoyed new freedom in their work, allowing them to focus their attention on new scientific breakthroughs.