What is the domain of f(x) = ln x?

• A. All real numbers
• B. x ≥ 0
• C. x < 0
• D. x > 0

Answer: (D)

When you see ln x, the input must be positive. The natural logarithm is defined only for positive x because it’s the inverse of the exponential function e^y, which always produces positive values. So ln x is defined for x > 0 (for example, ln 1 = 0 and ln e = 1). If x is zero or negative, ln x isn’t a real number. Therefore the domain is all x with x > 0, i.e., (0, ∞).