SOLUTION: When the number 𝑛 is written in base 𝑏, its representation is the two-digit number 𝐴𝐵 where 𝐴=𝑏−2 and 𝐵=2. What is the representation for 𝑛 in base (𝑏
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Question 1158010: When the number 𝑛 is written in base 𝑏, its representation is the two-digit number 𝐴𝐵 where 𝐴=𝑏−2 and 𝐵=2. What is the representation for 𝑛 in base (𝑏−1)?
Answer by KMST(5377) (Show Source): You can put this solution on YOUR website!
The value of a number in any base is really a polynomial.
If ABCD is how a number is written in base , its value is
.
Of course, if ABCD is how a number is written in base ,
we know that is an integer,
that is greater than A, B, C, and D,
and that would be written as 10 in base
The value of number 324 in base 10 is .
The value of the number written as in base is
, and we know that and .
So, and .
Substituting for and for , we get
Now we are dealing with polynomials.
-->-->-->-->
and that polynomial in is the value of the number that in base would be written as .
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