Question

If ${\log }_{2}N=a$ and ${\log }_{3}N=b$, where $2\le b<3$ 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)

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