(212)x =(23)10 where x is base (+ve integer), then the value of x is, number system
Answers
Answer:
1.5
Step-by-step explanation:
We may utilise the idea of translating integers from one base to another to get the base value of X in this equation. The two integers in this instance are (23)10, which is written in base 10, and (212)x, which is written in base x.
We must divide the number (23)10 by consecutive powers of x and record the remainders in order to convert it to base x. The digits of the resultant number are those of the number in base x, read from bottom to top. For instance:
(23)10 = 2x1 + 3x10^0 = 2x + 3x^0
Hence, the base x representation of the number (23)10 is 23x = 2x + 3x + 0 = 2x + 3.
We can now enter this number in the original equation as follows:
(212)x = 23x 2x^2 + x + 2 = 2x + 3
When we simplify this equation, we obtain:
2x^2 - x - 1 = 0
We may use the quadratic formula to find the value of x:
x = [-(-1) ± √((-1)^2 - 4(2)(-1))]
/(2(2)) x = [1 ± √(9)]
/4
As the base must be a positive integer, we take the positive root:
x = (1 + 3)/4 = 1.5
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