logarithm function
[logarithm function|logarithm function] is a mathematical function that maps positive real numbers to real numbers.
Definition
logarithm function is a mathematical function that maps positive real numbers to real numbers. The domain of logarithm function with base b is ( 0 , ∞ ). The range of logarithm function with base b is ( − ∞ , ∞ ).
Mechanism
logarithm function operates within a domain of ( 0 , ∞ ) and spans a range of ( − ∞ , ∞ ) for any base b. The base determines the specific behavior of the function. These mathematical properties define the input and output constraints of the logarithm function.
Causes
logarithm function The logarithm function's domain is restricted to positive real numbers, excluding zero. Its range spans all real numbers. The base of the logarithm function determines the specific behavior of the function.
Comparison
logarithm function When comparing the logarithm function to the exponential function, the roles of input and output are reversed. The exponential function takes an input and produces an output, while the logarithm function takes an output and produces an input. This relationship highlights how the two functions are inverses of each other. The switch in input and output positions is a key distinction between them.