Discussion

Explanation:

Given, $\left(\frac{4-{\log }_{2}n}{3-{\log }_{4}n}\right)$ < 0

Case 1: 4 – log₂n < 0 and 3 – log₄n > 0
⇒ log₂n > 4 and log₄n < 3
⇒ n > 16 and n < 64
∴ integral values of n can be 17, 18, …, 63 i.e., 47 values.

Case 2: 4 – log₂n > 0 and 3 – log₄n < 0
⇒ log₂n < 4 and log₄n > 3
⇒ n < 16 and n > 64
∴ No integral values of n is possible.

Hence, 47.

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