cat 2022 Question 14

Question

The number of distinct integer values of n satisfying $\frac{4-\log _2 n}{3-\log _4 n}\lt0$, is

Accepted Answer

Let $\log_2 n = y$

$\frac{4 - y}{3 - \frac{y}{2}}$ < $0$

$(4 - y)\left(3 - \frac{y}{2}\right)$ < $0$

$(4 - y)(6 - y)$ < $0$

$(y - 4)(y - 6)$ < $0$

$4$ < $y$ < $6$

$4$ < $\log_2 n$ < $6$

$2^4$ < $n$ < $2^6$

$16$ < $n$ < $64$

n can take values from 17 to 63 (inclusive).

Question 14.