Exponential equation turned into a quadratic in a^x

CAT has tested this idea 6 times across 6 papers, from 2017 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 2 · QA Q5	9^(…) − 4·3^(…) + 27 = 0; product of roots	B
CAT 2019 Slot 2 · QA Q1	2^(6x) + 2^(3x+2) − 21 = 0	A
CAT 2024 Slot 3 · QA Q22	10^x + 4/10^x = 17/2	A
CAT 2023 Slot 2 · QA Q2	three powers of 2 form a perfect square	C
CAT 2017 Slot 1 · QA Q24	9^(2x−1) − 81^(x−1) = 1944	B
CAT 2017 Slot 2 · QA Q25	powers of 9 and 4 grouped on each side	A

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