Compare powers by summing exponents or taking logs

CAT has tested this idea 4 times across 4 papers, from 2018 to 2025. Solve one, and the others are the same method with different numbers or wording, which is why repeated concepts are the most efficient thing to practise.

Question	What it asks	Answer
CAT 2025 Slot 1 · QA Q19	product of a_k^k vs product of later terms; smallest m	C
CAT 2021 Slot 3 · QA Q20	product of powers of 10^(1/7) exceeds 999	6
CAT 2018 Slot 2 · QA Q13	smallest n with 4^n > 17^19	B
CAT 2023 Slot 3 · QA Q7	5^(n−1) < 3^(n+1) < 2^(n+m)	5

Part of Logarithms & Exponents (55 questions since 2017).