Exponents and logarithms with fixed base and variable power play a surprisingly large role in real life. For example, there is a particular base e such that the slope of the exponent  is that exponent itself!
Properties of exponents  : Domain: all numbers. Range: positive numbers. If a (the base > 1, exponent is an increasing function, it is less than 1 for all negative x, and above 1 for all positive x. If a < 1, it is a decreasing function, gretaer than one for x < 0, and less than 1 for x gt& 0.
Properties of logarithms  : Domain: all non-negative numbers. Range: all numbers.  for all a. For a > 1: logarithm is an increasing function.  when x < 1,  when x > 1. For a < 1: logarithm is a decreasing function when x < 1, when x > 1.
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