Given that (292)₁₀ = (1204)ₓ in some number system x. The base x of that…

To find the base x, we expand the positional notation of (1204)ₓ. This equals 1·x³ + 2·x² + 0·x¹ + 4·x⁰, which simplifies to x³ + 2x² + 4. Setting this equal to the decimal value 292 gives the equation x³ + 2x² = 288. By testing integer values, we find that x=6 satisfies this: 6³ + 2(6²) = 216 + 72 = 288. Therefore, the base is 6. Option A (base 2) is immediately invalid because the digit '4' cannot exist in binary. Since the calculated base 6 does not match options A (2), B (8), or C (10), the correct choice is 'None of the above'.