a is the base of the exponential expression ax. a is also the base of the logarithmic expression logax.
Common Logarithmic Function
The logarithmic function f (x) = log10x.
x is the exponent in the exponential expression ax. It means a is multiplied by itself x times.
A function of the form f (x) = ax, where a > 0, a≠1, and x is any real number
The time it takes for a exponentially decaying substance to lose half its mass.
An expression of the form logax. If logax = b, ab = x.
A function of the form y = logax where x = ay, a > 0, and a≠1. This example is a logarithmic function with base a.
Natural Exponential Function
The function f (x) = ex.
Natural Logarithmic Function
The logarithmic function f (x) = logex = ln x.
|Change of Base||logax = , where a, b, and x are all positive real numbers and a, b≠1.|