The discussion centers on the limitations of logarithmic functions, specifically why the base x cannot be less than or equal to zero. It explains that the equation P = log_x(Q) translates to Q = x^P, raising concerns about defining expressions like x^{-1} or x^{1/2} when x is zero or negative. To avoid complications and the need for special definitions in these cases, logarithms are restricted to positive bases. This ensures consistency and clarity in mathematical definitions. Consequently, logarithmic functions are only defined for positive bases to maintain their validity.