floorlog101000

Floorlog101000 is a shorthand notation for the mathematical expression floor(log_10(1000)). It combines the floor function with the common logarithm base 10.

The floor function, denoted floor(x), returns the greatest integer less than or equal to x. The logarithm base 10, log_10(a), is the exponent to which 10 must be raised to obtain a; that is, log_10(10^k) = k.

For the specific values in floorlog101000, log_10(1000) equals 3 since 10^3 = 1000. Therefore, floor(log_10(1000)) equals floor(3), which is 3.

In a broader sense, floor(log_b(a)) (for a > 0 and b > 0, b ≠ 1) is the greatest integer k such that b^k ≤ a < b^(k+1). If a is exactly a power of the base, the floor equals the exponent. As a related note, the number of base-10 digits of a positive integer n is floor(log_10(n)) + 1; for 1000 this yields 3 + 1 = 4, reflecting its four digits.

These concepts appear in number theory and computer science, where logarithms help determine digit counts, place-value boundaries, and scalable ranges. The value of floor(log_10(1000)) being 3 is a direct consequence of 1000 = 10^3.