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If (211)x = (152)8 , then the value of base x is
- a)6
- b)5
- c)7
- d)9
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If (211)x= (152)8, then the value of base x isa)6b)5c)7d)9Correct answ...
2x^2 + x + 1 = 64 + 40 + 2
2x^2 + x + 1 = 106
x = 7
Most Upvoted Answer
If (211)x= (152)8, then the value of base x isa)6b)5c)7d)9Correct answ...
Given, (211)x= (152)8
To find the value of base x
Converting the given number to decimal format
(211)x = 2x² + 1.x + 1
(152)8 = 1.8² + 5.8 + 2 = 128 + 40 + 2 = 170
Equating the decimal values of both the numbers
2x² + x + 1 = 170
2x² + x - 169 = 0
Using the quadratic formula to solve for x
x = (-b ± √(b²-4ac))/2a
x = (-1 ± √(1+4(2)(169)))/(2(2))
x = (-1 ± √1361)/4
Since x is a positive integer, we take only the positive value of x
x = (-1 + √1361)/4 ≈ 6.99
Hence, the value of base x is 7.
To find the value of base x
Converting the given number to decimal format
(211)x = 2x² + 1.x + 1
(152)8 = 1.8² + 5.8 + 2 = 128 + 40 + 2 = 170
Equating the decimal values of both the numbers
2x² + x + 1 = 170
2x² + x - 169 = 0
Using the quadratic formula to solve for x
x = (-b ± √(b²-4ac))/2a
x = (-1 ± √(1+4(2)(169)))/(2(2))
x = (-1 ± √1361)/4
Since x is a positive integer, we take only the positive value of x
x = (-1 + √1361)/4 ≈ 6.99
Hence, the value of base x is 7.
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If (211)x= (152)8, then the value of base x isa)6b)5c)7d)9Correct answer is option 'C'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2026 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about If (211)x= (152)8, then the value of base x isa)6b)5c)7d)9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If (211)x= (152)8, then the value of base x isa)6b)5c)7d)9Correct answer is option 'C'. Can you explain this answer?.
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