What is a logarithm?

The logarithm base ##b## of a number ##n## is the number ##x## that when ##b## is raised to ##x##th power the resulting value is ##n##
##log_b n = x <=> b^x = n##
Example:
##log_2 8 = x##
##=> 2^x = 8##
##=> 2^x = 2^3##
##=> x = 3##
##log_5 1 = x##
##=> 5^x = 1##
##=> 5^x = 5^0##
##=> x = 0##