Question

If $\log _2 N = a$ and $\log _3 N = b$, where $2 \leq b <3$ and $a = b +1$, then the difference between largest and least integral values of $N$ is equal to

• A. 5
• B. 6
• C. 7
• D. 18

Answer 1

Answer: (B)

$ \log _2 N = a \Rightarrow N =2^{ a }$
$\Theta 3 \leq a <4 \Rightarrow 8 \leq N <16$
and $\log _2 N = b \Rightarrow N =3^{ b }$
$\Theta 2 \leq b <3 \Rightarrow 9 \leq N <27 $
$\therefore 9 \leq N <16$
$\therefore$ Difference of largest and least integral value of $N$
$=15-9=6 $