# Key Terms Chapter 10: Exponential and Logarithmic Functions

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

Example and Directions
Words (or words that have the same definition) The definition is case sensitive (Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pages] (Optional) Caption for Image (Optional) External or Internal Link (Optional) Source for Definition
(Eg. "Genetic, Hereditary, DNA ...") (Eg. "Relating to genes or heredity") The infamous double helix https://bio.libretexts.org/ CC-BY-SA; Delmar Larsen
Glossary Entries
Word(s) Definition Image Caption Link Source
common logarithmic function The function $$f(x)=\log{x}$$ is the common logarithmic function with base10, where $$x>0$$. $y=\log{x} \text{ is equivalent to } x=10^y$
logarithmic function The function $$f(x)=\log_a{x}$$ is the logarithmic function with base $$a$$, where $$a>0$$, $$x>0$$, and $$a≠1$$. $y=\log_a{x} \text{ is equivalent to } x=a^y$
natural logarithmic function The function $$f(x)=\ln(x)$$ is the natural logarithmic function with base $$e$$, where $$x>0$$. $y=\ln{x} \text{ is equivalent to } x=e^y$
asymptote A line which a graph of a function approaches closely but never touches.
exponential function An exponential function, where $$a>0$$ and $$a≠1$$, is a function of the form $$f(x)=a^x$$.
natural base The number $$e$$ is defined as the value of $$(1+\frac{1}{n})^n$$, as $$n$$ gets larger and larger. We say, as $$n$$ increases without bound, $$e≈2.718281827...$$
natural exponential function The natural exponential function is an exponential function whose base is $$e$$: $$f(x)=e^x$$. The domain is $$(−∞,∞)$$ and the range is $$(0,∞)$$.
one-to-one function A function is one-to-one if each value in the range has exactly one element in the domain. For each ordered pair in the function, each $$y$$-value is matched with only one $$x$$-value.