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)
Explanation: Given, (12x)3 = (123)x
Since LHS has 3 as the base and RHS has ‘x’ base,
1 * 3*3 + 2 * 3 + x * 1 = 1 * x*x + 2 * x + 3 9 + 6 + x = x2 + 2x + 3 x2 + x - 12 = 0 x2 + 4x - 3x - 12 = 0 x( x + 4 ) - 3(x + 4) = 0 (x + 4)(x - 3) = 0 x = 3, -4
But, both the values are infeasible.
Alternative explanation –
According to the rules of number systems , the numbers present in a number system should not be greater than the base of the number system.
According to LHS , (12x)3 tells us that the value of x should be less than 3.
According to RHS , (123)x tells us that the value of x should be greater than 3 as largest digit in 123 is 3.
Therefore, any combination is not possible.
So, option (D) is correct.
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