Why do general logarithmic function equation have restrictions on the value of b?

A function is any process that takes an input and gives a single output value. A square root is not a function because it gives two outputs for each input. A logarithm is a function, but only if the input is positive greater than zero.

log(base a)(b) = x means b = a^x and it is impossible to express zero or a negative value of b by that process.