Logarithms are used to make long and complicated calculations easy. The logarithm is related to exponents or indices. I.e., while ab=c is called the exponential form, logac=b is called the logarithmic form. In math, the logarithm is the inverse operation to exponentiation. That means the logarithm of a number is the exponent to which another fixed number, the base, must be raised to produce that number. In simple cases, the logarithm counts factors in multiplication. For example, the base 10 logarithm of 1000 is 3, like 10 to the power 3 is 1000 (1000 = 10×10×10 = 103)
John Napier introduced logarithms in the early 17th century as a means to simplify calculations. Navigators rapidly adopted them, scientists, engineers, and others to perform computations more easily, using slide rules and logarithm tables. Table look-ups and simpler addition can replace tedious multi-digit multiplication steps because of the fact - important in its own right - that the logarithm of a product is the sum of the logarithms of the factors:
logb(xy) = logb(x) + logb(y)
Then the logarithmic function is given by; f(x) = log b x = y, where b is the base, y is the exponent and x is the argument.