Exponential and Logarithmic Functions

The now ubiquitous term gigabyte, which may, in fact, become a metonymy for the first decade of the twenty-first century, has been defined as a mathematical exponential expression looking like .  This is read as the base number    to the exponent   (meaning multiplied together  times). Moreover, according to Dictionary.com, the gigabyte is “roughly the amount of data required to encode a human gene sequence (including all the redundant codons).”

While single numeric expressions can be interesting in their own right and highly significant in some contexts (consider the numbers and   ), it is their algebraic contexts  or functional generalizations which provide insights into the workings of the mathematics behind the phenomena. Functions, for example, exhibit relationships between two or more quantities which can then uncover patterns of behavior as the numbers change. Their graphs allow us a means of visualizing these changes. This, in turn, can provide a basis for certain kinds of predictions, both into the future and also reaching back into the past. That is why it is important to study both exponential expressions and their counterpart logarithmic expressions as functions of a single variable.

Last Updated by SAS October 07, 2026, 16:00:34