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Consider the equation (123)5 = (x8)y with x and y as unknown. THe number of possible solutions is ______.
Correct answer is '3'. Can you explain this answer?
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Verified Answer
Consider the equation (123)5 = (x8)ywith x and y as unknown. THe numbe...
Changing (123) base 5 into base 10= 1*25+2*5+3*1=38
Changing x8 base y in decimal= x*y+8
Equating both we get xy+8=38
xy=30
possible combinations =(1,30)(2,15),(3,10)
but we have ‘8’ present in x8 so base y>8 as all three are satisfying the conditions so total solutions =3
Most Upvoted Answer
Consider the equation (123)5 = (x8)ywith x and y as unknown. THe numbe...
Solution:
Given equation is (123)5 = (x8)y
We need to find the number of possible solutions for x and y.
To solve this equation, we need to convert (123)5 into base 8.
Conversion of (123)5 into base 8:
We can convert (123)5 into base 10 first and then into base 8.
(123)5 = 1*5^2 + 2*5^1 + 3*5^0
= 25 + 10 + 3
= 38
Now, we can convert 38 into base 8.
38/8 = 4 remainder 6
4/8 = 0 remainder 4
Therefore, (123)5 = (46)8
Now, we can substitute this value in the given equation.
(46)8 = (x8)y
We can see that the only possible values for x and y are:
x = 4 and y = 2
x = 6 and y = 1
x = 8 and y = 0
Therefore, the number of possible solutions for x and y is 3.
Given equation is (123)5 = (x8)y
We need to find the number of possible solutions for x and y.
To solve this equation, we need to convert (123)5 into base 8.
Conversion of (123)5 into base 8:
We can convert (123)5 into base 10 first and then into base 8.
(123)5 = 1*5^2 + 2*5^1 + 3*5^0
= 25 + 10 + 3
= 38
Now, we can convert 38 into base 8.
38/8 = 4 remainder 6
4/8 = 0 remainder 4
Therefore, (123)5 = (46)8
Now, we can substitute this value in the given equation.
(46)8 = (x8)y
We can see that the only possible values for x and y are:
x = 4 and y = 2
x = 6 and y = 1
x = 8 and y = 0
Therefore, the number of possible solutions for x and y is 3.
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Consider the equation (123)5 = (x8)ywith x and y as unknown. THe number of possible solutions is ______.Correct answer is '3'. Can you explain this answer?
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