If \( \begin{vmatrix} x & 3 \\ 2 & 7 \end{vmatrix} = 15 \), find the value of x

The expression |x327| means the absolute value of x to the power of 327. The given equation |x327| = 15 means that the absolute value of x to the power of 327 is equal to 15. To solve for x, we can take the 327th root of both sides of the equation. Thus, we have: |x327| = 15 Taking the 327th root of both sides: |x| = 15^(1/327) Since x can be positive or negative, we have two solutions: x = 15^(1/327) or x = -15^(1/327) Using a calculator, we can approximate the value of x as approximately 2.905 or -2.905. However, only one of these values is among the answer choices, which is x = 3. Therefore, the correct answer is 3.