When two logarithms of the same base are subtracted, the arguments of each logarithm are divided. For example, if two logarithms of base 10 with arguments of 10 and 2 are subtracted, the expression is resolved to a single logarithm of base 10 with an argument of 5.
Logarithms are a form of inverse exponents. Raising 2 to the third power, also known as multiplying 2 by 2 by 2, equals 8. If 2 raised to the third power equals 8, then a logarithm with base 2 and an argument of 8 equals 3. In the case of exponents and logarithms, the base is the same.
The mathematical precursors of logarithms were first studied by the Babylonians in 20th century B.C. These theories were later refined and expanded by the eighth century Indian mathematician Virasena. He developed tables of logarithms to bases 2, 3 and 4. In 1614, Scottish mathematician John Napier first coined the term "logarithm" in a published work, having spent 20 years studying the field. He found that by computing logarithmic tables, he arrived at a precise definition of the ratio that comprises a logarithm. Logarithms have widespread applications beyond mathematics; they are used in astronomy, music theory and psychology.