The base (or radix) of the number system such that the following equation holds is____________.
312/20 = 13.1
(A) 3
(B) 4
(C) 5
(D) 6
Answer: (C)
Explanation: Let x (≠ 0) be the base of the given equation.
We have,
LHS = ( 3x2 + x + 2 ) / ( 2x) = ( 3x / 2 ) + ( 1 / 2 ) + ( 1 / x )
RHS = x + 3 + ( 1 / x )
Now, for the equation to hold true, LHS = RHS
( 3x / 2 ) + ( 1 / 2 ) + ( 1 / x ) = x + 3 + ( 1 / x )
⇒ 3x + 1 = 2x + 6
⇒ x = 5
So, the base is 5.