Logaritma Fonksiyonunun İrrasyonel Fonksiyon İle Temsili ve Bu Temsile Dayalı Üstel Fonksiyon Elde Edilmesi Üzerine

Year 2021, Issue: 25, 542 - 549, 31.08.2021

Müslüm Özışık

https://doi.org/10.31590/ejosat.930694

Abstract

Bu çalışmada matematikte çok yaygın bir kullanım alanına sahip olan en temel fonksiyonlardan olan logaritma fonksiyonunun irrasyonel bir fonksiyon ile temsil edilmesi üzerine çalışılmıştır. Bu amaçla logaritma fonksiyonu yerine kullanılabilecek irrasyonel bir fonksiyon önerisi yapılmış, uygun matematik ve nümerik analiz tanım ve yöntemleri çerçevesinde önerilen fonksiyon elde edilmiştir. Elde edilen irrasyonel fonksiyon üzerinden ters fonksiyonu oluşturulmak suretiyle üstel fonksiyonlar için yeni bir yaklaşım elde edilmiştir. Sayısal sonuçlar ve grafikler elde edilerek gerekli değerlendirmeler yapılmıştır.

Keywords

Logaritma, Doğal Logaritma, Napier, Euler

On the Representation of the Logarithm Function by the Irrational Function and the Obtaining of an Exponential Function Based on This Representation

Abstract

In this study, the representation of the logarithm function, which is one of the most basic functions that has a very common usage area in mathematics, has been studied with an irrational function. For this purpose, an irrational function that can be used instead of a logarithm function has been proposed, and the proposed function has been obtained within the framework of appropriate mathematical and numerical analysis definitions and methods. A new approach has been obtained for exponential functions by constructing the inverse function on the obtained irrational function. Necessary evaluations were made by obtaining numerical results and graphics.

Keywords

Logarithm, Natural Logarithm, Napier, Euler

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