There are a number of rules known as the laws of logarithms. These allow expressions involving logarithms to be rewritten in a variety of different ways. The laws apply to logarithms of any base but the same base must be used throughout a calculation.

Suppose

x = a^m and y = aⁿ,
then the equivalent logarithmic forms are
log_a x = m and log_a y = n.
Using the product property of indices, we get
xy = a^m × aⁿ = a^m+n.