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##