CAT 2023 Inequalities Question (Hard)

Question

Let be any natural number such that . Then, the least integer value of that satisfies for each such , is

Accepted Answer

Step-by-Step Solution Step 1 Simplify the First Inequality We are given the inequality 5 n-1 3 n 1 To solve this, we take logarithms on both sides. For simplicity, let s use logarithm base 5 log_5 5 n-1 log_5 3 n 1 This simplifies to n - 1 n 1 log_5 3 Rearrange the terms n - n 1 log_5 3 1 Simplify f

CAT 2023

Quantitative

Inequalities

Hard

Let $n$ be any natural number such that $5^{n-1} \lt 3^{n+1}$ . Then, the least integer value of $m$ that satisfies $3^{n+1} \lt 2^{n+m}$ for each such $n$ , is

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