The Limited Logarithm: Why x Can't Be <= 0

[roni1]

Why x can't be less or equal to zero?

 

[HOI]

Why x can't be less or equal to zero?

$$P= log_x(Q)$$ is equivalent to $$Q= x^P$$. How, exactly, would you define $$x^{-1}$$ if x were equal to 0? How would you define $$x^{1/2}$$ if x were -1? In order that we not have to give special definitions to cases like those, we only define the exponential for positive base. And from that, logarithm can only be defined for positive base.