CAT 2022 Logarithms Question (Medium)

Question

The number of distinct integer values of satisfying , is

Accepted Answer

To solve the inequality 3 - log_4 n 0 positive . - If n 16, then log_2 n 4, hence the numerator 4 - log_2 n 0 positive . - If n 64, then log_4 n 3, hence the denominator 3 - log_4 n 64 denominator negative - not possible . - Case 2 Numerator is negative and denominator is positive - This occurs when

CAT 2022

Quantitative

Logarithms

Medium

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

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