What is the domain of F(x) = In (x)? A: all real numbers except 0
B: all real numbers
C: all real numbers less than 0
D: all real numbers greater than 0

In terms of symbols, we would write

The natural log function, or any log function, is not defined for x = 0 or any negative x value.

Consider the form which is equivalent to and notice how the y value slowly approaches zero but never actually gets there. That is one way to see why the inputs of any log function must be larger than 0.