Logarithms are the inverse functions of exponentials. With two exceptions, they look like where a is the base. This means that . In other words, the value of a logarithm (or log, for short) is the power to which the base must be raised in order to get the number you are taking the log of. For example, since . The two exceptions in form are the common log, which has an understood base of 10, written , and the natural log, which has base e, and is written . Note that is only defined for x > 0. There is, in fact, an asymptote at x = 0 and this function will pass through the point (1,0).
Log functions have the following properties.