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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

Logarithms are defined as real numbers.they are excellent to work with large and difficult exponents.