Final answer:
To solve the equation 1094 [log(2x)] = 1, we isolate log(2x), convert it back to exponential form, and solve for x. The value of x should be approximately 1/2, but the given options do not match this solution, indicating a possible error in the question.
Step-by-step explanation:
To find the true solution to the logarithmic equation 1094 [log(2x)] = 1, we need to solve for x. First, divide both sides by 1094 to isolate the logarithm:
log(2x) = 1/1094
Next, we use the property that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers, but since there is only one logarithm of a single product here, we'll move to the inverse operation to remove the logarithm:
10^(log(2x)) = 10^(1/1094)
Using the fact that the base-10 logarithm and the base-10 exponentiation are inverse operations, we have 2x = 10^(1/1094). Now calculate the value of 10^(1/1094) using a calculator.
Assuming the value is approximately 1 (since 1/1094 is a very small number), we get:
2x ≈ 1
Divide both sides by 2:
x ≈ 1/2
However, none of the options a-d given in the question correctly matches this solution. It is possible that there is a typo in the given options or the original equation. To address this question accurately, it would be necessary to revisit the initial problem to ensure that it is presented correctly.