Question

Let $lo{g}_{M}N=\alpha +\beta$, where $\alpha$ is an integer and $\beta$ is non negative fraction. If M and $\alpha$ are prime and $\alpha +M=7$ the $N\in [a,b]$. The absolute value of $(b-5a)$ can be

• A. 0
• B. 24
• C. 48
• D. 96

Answer 1

Answer: (A)

0

$lo{g}_{M}N=\alpha +\beta$
$M,\alpha$ are prime
$\alpha +M=7$
So, if $\alpha =2,\alpha =5$
$\alpha =5,M=2$
Case I- $\alpha =2$
$M=5$
$lo{g}_{5}N=2+\beta$
$N=5^{(2+\beta )}$
So, $Nϵ[25,125]$
Case II- $\alpha =5,M=2$
$N=2^{(5+\beta )}$
$Nϵ[32,64]$
So, $Nϵ[25,125]$
$a=25$
$b=125$
$b-5a=0$