Tag: math & puzzles

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.

To solve this question, the user needs to know the basics of algebraic equations and the concept of squares.

Let's assume that the negative integer is represented by the variable x. The sum of the square of a negative integer and itself can be represented by the equation:

$x^2 + x = 0$

We can factor out x from this equation:

$x(x + 1) = 0$

Thus, either x = 0 or x + 1 = 0.

If x = 0, then $x^2 + x = 0^2 + 0 = 0$, which satisfies the given condition.

If x + 1 = 0, then x = -1, and $x^2 + x = (-1)^2 + (-1) = 1 - 1 = 0$, which also satisfies the given condition.

Therefore, the answer is either A (-1) or C (0), as these are the values of x that satisfy the equation.

Option A (-1) and Option C (0) are both correct answers because the equation is satisfied by both values of x.

Option B (-2) is incorrect because this value does not satisfy the equation.

Option D (-1/2) is incorrect because it is not an integer and it does not satisfy the equation.

The Answer is: A or C