section_path: Analytic properties
section_name: Analytic properties
paragraph_text: Analytic properties
  
  A deeper study of logarithms requires the concept of a function. A function is a rule that, given one number, produces another number. An example is the function producing the x -th power of b from any real number x, where the base b is a fixed number. This function is written as f (x) = b. When b is positive and unequal to 1, we show below that f is invertible when considered as a function from the reals to the positive reals.