Logarithms were first used in India in the 2nd century BC. The first to use logarithms in modern times was the German mathematician Michael Stifel (around 14871567). In 1544, he wrote down the following equations: formula_3 and formula_4. This is the basis for understanding logarithms. For Stifel, formula_5 and formula_6 had to be whole numbers. John Napier (1550–1617) did not want this restriction, and wanted a range for the exponents.