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Consider the equation (43)x = (y3)8 where x and y are unknow. The number of possible solutions is _____
Correct answer is '5'. Can you explain this answer?
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Verified Answer
Consider the equation (43)x = (y3)8where x and y are unknow.The number...
(43)x = (y3)8
Since a number in base -k can only have digits from 0 to (k-1), we can conclude that: x > 5 and y < 7
Now, the original equation, when converted to decimal base gives:
Now, the original equation, when converted to decimal base gives:
So, we have the following constraints:
The set of values of (x,y) that satisfy these constraints are:
I am counting 5 pairs of values.
Most Upvoted Answer
Consider the equation (43)x = (y3)8where x and y are unknow.The number...
Explanation:
Given equation is:
(43)x = (y3)8
We need to find the number of possible solutions for x and y.
Step 1: Express the equation in terms of prime factors
(43)x = (y3)8
= (43)x = (y8)3
= 43x = 3 × (y8)
Step 2: Apply the fundamental theorem of arithmetic
Since both sides of the equation have unique prime factorization, we can conclude that:
- 43 must divide 3, which is not possible since 43 is a prime number and 3 is not a multiple of 43.
- Therefore, there are no solutions for x and y that satisfy the equation.
Step 3: Conclusion
Hence, the number of possible solutions for x and y is 0.
Therefore, the correct answer is 0.
Given equation is:
(43)x = (y3)8
We need to find the number of possible solutions for x and y.
Step 1: Express the equation in terms of prime factors
(43)x = (y3)8
= (43)x = (y8)3
= 43x = 3 × (y8)
Step 2: Apply the fundamental theorem of arithmetic
Since both sides of the equation have unique prime factorization, we can conclude that:
- 43 must divide 3, which is not possible since 43 is a prime number and 3 is not a multiple of 43.
- Therefore, there are no solutions for x and y that satisfy the equation.
Step 3: Conclusion
Hence, the number of possible solutions for x and y is 0.
Therefore, the correct answer is 0.
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Consider the equation (43)x = (y3)8where x and y are unknow.The number of possible solutions is _____Correct answer is '5'. Can you explain this answer?
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