Key Terms Chapter 10: Exponential and Logarithmic Functions
- Page ID
- 102257
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| 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 |
| 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. |