Final answer:
The log equation log x 4 = -2 corresponds to x^-2 = 4. By converting to an exponential equation and solving for x, we find that x = 4 is the correct answer.
Step-by-step explanation:
The equation log x 4 = -2 can be solved by understanding the basic properties of logarithms. Here, the base of the logarithm is x and the value is -2, which means that x to the power of -2 is equal to 4. Transforming the logarithmic equation to an exponential equation, we get x^-2 = 4. This can also be written as 1/x^2 = 4. By solving for x, we find that x squared is equal to the reciprocal of 4, which is 1/4. Hence, x is equal to the square root of 1/4, which simplifies to 1/2.
As 1/2 squared is 1/4, we need to find a number that when squared gives us 1/4 inverted, which is 16. Therefore, x must be either 4 or -4. But since we deal with logarithms, which typically assume positive values for the base, the factor -4 is dismissed. Therefore, the value of x that satisfies the given equation is 4. The correct option is d) x = 4.