1. The problem asks: What kind of number are all in the x-coordinates of a logarithmic function? 2. A logarithmic function generally has the form $y = \log_a(x)$ where $a > 0$ and $a \neq 1$. 3. The domain of a logarithmic function is all positive real numbers, i.e., $x > 0$. This means that every valid $x$-coordinate must be a positive real number. 4. Let's analyze the choices: - Natural numbers ($1, 2, 3, \ldots$) are a subset of positive real numbers but do not include all possible positive real values. - Integers include negative numbers and zero, which are not in the domain of the logarithm. - Rational numbers (fractions and integers) are also positive numbers when positive, but the logarithm can accept irrational positive numbers too. - Whole numbers (natural numbers including zero) include zero, which is outside the domain. 5. Therefore, all $x$-coordinates for a logarithmic function are positive real numbers, which include but are not limited to natural numbers, rational numbers, and irrational numbers. The important condition is $x > 0$.