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Exponential and logarithmic functions and their application in mechanical engineering

The paper studies exponential and logarithmic functions that are mutually inverse functions. These functions appear throughout history from Archimedes who dealt with potencies to Euler who defined logarithm, and Napier who compiled the first logarithmic tables. Exponential and logarithmic functions are one of the elementary functions used in arithmetic operations and compositions of other elementary functions. The definition of exponential and logarithmic functions requires knowledge of their properties and graphical representation. The application of exponential and logarithmic functions is very wide. There are many scope that apply exponential and logarithmic functions to solve their problem tasks from physics, geodesy, biology, economics to forensics. Through examples, the authors will show their application in problem tasks in the wider field of mechanical engineering. The importance and purpose of the Taylor equation in determining the stability of tools in machining will be presented. The properties of exponential and logarithmic functions will be applied through examples related to the elementary theory of plasticity, ie through the force of deformation, Sachs and Siebel equations to logarithmic deformation.

exponential and logarithmic functions, mechanical engineering, Taylor equation, logarithmic deformation

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