The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e, where e is equal to 2.718281828459...
In other words, the logarithmfunction is a bijection from the set of positive real numbers to the set of all real numbers.
Logarithms can be defined to any positive base other than 1, not just e, and they are always useful for solving equations in which the unknown appears as the exponent of some other quantity.