The number of distinct integer values of n satisfying \frac{4-\log2 n}{3-\log 4 n} < 0 , is

CAT 2022 Slot 2 Paper

Question : 63 of 66

Marks: +1, -0

The number of distinct integer values of $n$ satisfying ${4-\log2 n}/{3-\log 4 n} < 0$ , is

Solution:

Let

\log _2 n=y

{4-y}/{3-\;{y}/{2}}< 0

(4-y) (3-\;{y}/{2}) < 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).
The number of

n

values possible

=47

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