Multiple choice

What is the value of x provided (12x) base3 = (123)x?

  1. 2

  2. 3

  3. 5

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Left side: (12x)_3 = 1 * 3^2 + 2 * 3^1 + x * 3^0 = 9 + 6 + x = 15 + x. Right side: (123)_x = 1 * x^2 + 2 * x^1 + 3 * x^0 = x^2 + 2x + 3. Solving: 15 + x = x^2 + 2x + 3, so x^2 + x - 12 = 0, giving x = 3 or x = -4. Since base must be > 3 (digit 3 present), x = 3.

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