Logarithms are defined as the inverse of exponents. Just like exponents, logarithms can have any base however the most common bases are ten (since we use a base ten number system) and e (the natural logarithm). The logarithm of a number in base a, is defined to be the number that a must be raised to to get that number. For example:
log2 2 = 1 log3 3 = 1
log2 4 = 2 log3
9 = 2
log2 8 = 3 log3 27 = 3
Logarithms make smaller numbers from larger numbers, thus reducing calculations by a fair amount. However, more importantly, logarithms reduce multiplications to additions, divisions to subtractions and powers to multiplications as follows.
log (x.y) = log (x) + log (y)
log (x/y) = log (x) – log (y)
log (x y) = y log (x)
Once a solution has been found to the problem the antilog can be found to give the correct answer.