An exponential function is a mathematical function of the following form:
f ( x ) = a x
where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828. Thus, the above expression becomes:
f ( x ) = e x
When the exponent in this function increases by 1, the value of the function increases by a factor of e . When the exponent decreases by 1, the value of the function decreases by this same factor (it is divided by e ).
In electronics and experimental science, base-10 exponential functions are encountered. The general form is:
f ( x ) = 10 x
When the exponent increases by 1, the value of the base-10 function increases by a factor of 10; when the exponent decreases by 1, the value of the function becomes 1/10 as great. A change of this extent is called one order of magnitude.
For a given, constant base such as e or 10, the exponential function "undoes" the logarithm function, and the logarithm undoes the exponential. Thus, these functions are inverses of each other. For example, if the base is 10 and x = 3:
log (10 x ) = log (10 3 ) = log 1000 = 3
If the base is 10 and x = 1000:
10 (log x) = 10 (log 1000) = 10 3 = 1000