CAT 2022 Slot 2 QA Question 8: The number of distinct integer values of $n$ satisfying $\dfrac{4 - \log_2 n}{3 - \log_4 n}

Question

The number of distinct integer values of $n$ satisfying $\dfrac{4 - \log_2 n}{3 - \log_4 n} < 0$, is

Accepted Answer

Let $y = \log_2 n$. Then $\log_4 n = \dfrac{y}{2}$.

$\dfrac{4 - \log_2 n}{3 - \log_4 n} 
$\dfrac{4 - y}{3 - \dfrac{y}{2}} 
$\dfrac{4 - y}{6 - y}

The critical values are $y = 4$ and $y = 6$. The fraction is negative when the numerator and denominator have opposite signs.

$4 
$4 
$16

Thus, $n$ c

The number of distinct integer values of nnn satisfying 4−log⁡2n3−log⁡4n<0\dfrac{4 - \log_2 n}{3 - \log_4 n} < 03−log4​n4−log2​n​<0, is