Logarithm with base . The logarithm of with base , denoted by , is defined as the unique value satisfying . In other word we have
Common and natural logarithms. The common logarithm of (denoted by ) and the natural logarithm of (denoted by ) are defined respectively by
Logarithmic function. Let be a positive real value. A function is called an logarithmic function with base if
Properties of logarithmic functions. The logarithmic function is a one-to-one function; thus, implies . Furthermore, (2) indicates that is the inverse function of the exponential function .
Natural logarithmic function. A function is called the natural logarithmic function if