Combination of n Different Things Taken One or More at a Time
Let logMN=α...
Question
Let logMN=α+β, where α is an integer and β is non negative fraction. If M and α are prime and α+M=7 the N∈[a,b]. The absolute value of (b−5a) can be
A
0
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B
24
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C
48
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D
96
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Solution
The correct option is B 0 logMN=α+β M,α are prime α+M=7 So, if α=2,α=5 α=5,M=2 Case I- α=2 M=5 log5N=2+β N=5(2+β) So, Nϵ[25,125] Case II- α=5,M=2 N=2(5+β) Nϵ[32,64] So, Nϵ[25,125] a=25 b=125 b−5a=0