Exponential and Logarithmic Functions

Exponential functions are functions that contains a variable exponent and can be written on the form $y=a\cdot b^x,$ where $a$ and $b$ are constants. In this chapter the constant number $e$ is introduced. This constant is often referred to as the natural base and it allows for a special case of exponential functions, natural base exponential functions, to be introduced.
Various transformations of exponential functions and how they affect the graphs and the equations are introduced. The transformations that in the chapter are explored include vertical and horizontal translations, reflections in the $x\text{-}$ and in the $y\text{-}$axis and stretching and shrinking of the functions.
The inverse function to exponential functions are logarithmic functions. This chapter explores various aspects of the inverse relationship between exponential and logarithmic functions.
Logarithms can be written in logarithmic form and in exponential form. A logarithm with the base $10$ is often referred to as the common logarithm. When the base of the logarithm is $e$ the name natural logarithm is commonly used.
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Subchapters:

• Exponential Functions
• The Natural Base e
• Transformations of Exponential Functions
• Evaluating Logarithms
• Graphing Logarithmic Functions
• Solving Exponential Equations