Logarithms are a good way to work with quantities with big or complicated exponents. These are defined for real numbers.
suppose we have y = x^a then a is said to be the logarithm of y with respect to base x. It is written as
LOG y = a x is written as a subscript to LOG. y must be > 0 .
The other way, if a is logarithm of y with respect to x, then x^a = y. x is called base.
suppose you have y = x^21 x raised to power 21. Such relationships are easily expressed in logarithms with simple numbers and relations.
y = x^21 we apply logarithm function on both sides of =, we get
log y = log x^21 this also written as 21 * log x
The original complicated y = x^21 is simplfied as
log y = 21 log x