If there are two logarithms added together with similar base number, the sum will be equivalent to the logarithm of the two numbers’ product. For instance, "log2 16 + log2 1" can be simplified into log2 (16 x 1), or log2 16, which is 4.

The addition property of the logarithm indicates that the reverse is correct as well: the logarithm of a value can be rewritten as the sum of the logarithm of its factors. The log3 81 exp​ression, for instance, can be rewritten into log3 3 + log3 27. The derivation of this addition property is from an exponential property so that am x an = a (m+n).

The logarithmic subtraction property shows that the difference of two equal-base logarithms can be rewritten into the logarithm of the two numbers’ quotient. The exp​ression log5 125 - log5 5, for instance, can be simplified into the log5 25, from log5 (125/5), which is equivalent to 2.

The derivation of the logarithmic subtraction property is from an exponential property so that am - an = a (m-n). Both of these addition and subtraction properties of logarithms are usually introduced to students in their Algebra 2 subject. This lesson allows them to learn about the relationships between logarithms and exponents.