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Key Terms Chapter 10: Exponential and Logarithmic Functions

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    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
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    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.        
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