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E-STAR - Student
E-Lecture - Laws and Properties of Logarithms

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