If (12x)_3 = (123)_x, then the value of x is
- A. 3
- B. 3 or 4
- C. 2
- D. None of these
Answer: D. None of these
Explanation: LHS base 3 implies digits < 3 (so x < 3). RHS base x implies digits < x (so x > 3). This is a contradiction. Thus no such x exists. (Technically in base 3, digits are 0,1,2. If x is a digit it must be 0,1,2. But RHS base x must be > 3). Wait, (12x) means digits 1, 2, x. For this to be valid in base 3, x must be 0, 1, or 2. If x=2, LHS=(122)_3 = 9+6+2=17. RHS=(123)_2 impossible (digit 3 in base 2). The conditions on x are conflicting.