To solve this problem, we need to understand the concept of logarithms and how they relate to exponents and exponentiation.

The problem states that the logarithm (base ten) of five hundred times an integer is three. We can write this information as:

log10(500x) = 3

To find the value of x, we need to isolate it on one side of the equation. We can do this by exponentiating both sides of the equation with base 10:

10^(log10(500x)) = 10^3

500x = 1000

Now, we can solve for x by dividing both sides of the equation by 500:

x = 1000/500

x = 2

Therefore, the correct answer is D. 2.