if 2N4 base7 = 15N base9. find the value of N
Answers
Answer:
← BACK PRINT + TEXT SIZE – SEARCH HOME
search
Question from koteawarao, a teacher:
Find a base 7 three-digit number which has its digits reversed when expressed in base 9.
ans: (281) base 7 and (182) base 9
Koteawarao,
When you are working in base 7 the only "digits" allowed are 0, 1, 2, 3, 4, 5 and 6. In your answer you have the digit 8 so the answer given can't be correct. The symbol 8 has no meaning in base 7.
To solve your problem you want digits a, b and c so that
abc7 = cba9
where a, b and c are either 0, 1, 2, ... ,6. Using the definition of numbers expressed in different bases this can be written
a × 72 + b × 7 + c = c × 92 + b × 9 + a
On simplification this becomes
4(6a - 10c) = b
Hence 4 divided b and since b = 0, 1, ..., 6 either b = 0 or b = 4.
If b = 0 then 6a = 10c. You know that a and c are between 0 and 6 so what values of a and c make 6a = 10c? Check the values you obtained for a, b and c solve the problem.
If b = 4 then 6a - 10c = 1. Check all possible values of a and c. Do you find a solution.
I found two choices for a, b and c that solve the problem.
Harley
HEY MATE HERE IS YOR ANSWER:-
100×2 + 10×n + 4 = 100×1 + 10×5 + n
200 + 4 -100 - 50 = n -10n
54= 9 n
n = 54/9
n = 6