Determine the value of base b if (152)b = 0x6A. Please show all steps.
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he value of base b if (152)b = 0x6A. = 8
Step-by-step explanation:
Determine the value of base b if (152)b = 0x6A. Please show all steps.
0x6A = (6A)₁₆ = 6 * 16¹ + A*16⁰ = 96 + 10 = 106 ( A = 10 in Hexadecimal)
(152)b = 1 * b² + 5 * b¹ + 2 * b⁰
=> (152)b = b² + 5b + 2
Equating both
=> b² + 5b + 2 = 106
=> b² + 5b - 104 = 0
=> b² + 13b - 8b - 104 = 0
=> b(b+13) - 8(b + 13) = 0
=> (b-8)(b+13) = 0
b = 8 ( b ≠ - 13 as base can not be negative)
so b = 8
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