Chained logs telescope via change of base

CAT has tested this idea 3 times across 3 papers, from 2020 to 2024. 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.

QuestionWhat it asksAnswer
CAT 2024 Slot 3 · QA Q163^a = 4, 4^b = 5, …, 8^f = 9; product abcdef2
CAT 2020 Slot 3 · QA Q10products of log_2 4, log_4 8, log_8 16 powers24
CAT 2020 Slot 1 · QA Q5log_4 5 = log_4 y × log_6 √536

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