Homework properties of logarithms

The Definition of a Logarithm. In college, especially in mathematics and physics, log x consistantly means log ex. A popular notation (despised by some) is: ln x means log ex . To calculate logs to other bases, the change of base rule below (#4) should be used. It is only multiplication by a constant (1 / log ab ).

These four basic properties all follow directly from the fact that logs are exponents. In words, the first three can be remembered as: The log of a product is equal to the sum of the logs of the factors. The log of a quotient is equal to the difference between the logs of the numerator and demoninator.

The log of a quotient is equal to the difference between the logs of the numerator and demoninator. The log of a power is equal to the power times the log of the base. Additional properties, some obvious, some not so obvious are listed below for reference. Number 6 is called the reciprocal property. log b 1 = 0. log bb = 1. log bb2 = 2.

The log of a power is equal to the power times the log of the base. Additional properties, some obvious, some not so obvious are listed below for reference. Number 6 is called the reciprocal property. log b1 = 0. log bb = 1. log bb 2 = 2. log bb x = x.