TITLE: Why must the base of a logarithm be a positive real number not equal to 1?
QUESTION [43 upvotes]: Why must the base of a logarithm be a positive real number not equal to 1? and why must $x$ be positive?
Thanks.

REPLY [2 votes]: I think you can take a log of a negative number depending on the base.  for example, solve the solution of〖-2〗^x=-8   which can be rewritten as 〖log〗_(-2) (-8)=3