Algebra: Exponent and logarithm as functions of power

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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