International Conference on Applied Analysis and Mathematical Modeling ICAAMM19, İstanbul, Turkey, 10 - 13 March 2019, pp.234
: It is known that exponential functions are one of the most general functions for calculus and science. It has widespread use in both mathematics and science. (It can be used in the modeling of many events such as population growth, compound interest calculation, investment increase, earthquake, etc.). Therefore, it is not possible to think of logarithms independent of the above. For this reason, it would not be wrong to say that exponential operations are among the major issues in the early 1500s and early 1600s. John Napier (1550-1617), Henry Briggs (1551-1630) and Joost Bürgi (1552-1632) are the scientists among those dealing with exponential processing with this approach. Napier and Bürgi are generally known with the invention of exponential functions, what they actually created is quite different from modern exponential functions. Also known as logarithms, exponential functions are used in many different disciplines, from calculus to probability, statistic, astronomy, physics, chemistry etc. Napier developed his logarithm theory based upon algebra, while Bürgi developed his based on geometry. The commonly known exponential function is defined as a base number with a raised exponent, also known as a power. They have also been engaged in logarithm and antilogarithm, and have made the basis for today's logarithm phenomena and tables.
In this study, irrational function suggestion (S(x))
rather than function which is used as exponential function has been emphasized
and a general irrational function has been obtained and the results obtained
with both functions are compared.