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IPMAT Indore 2023 - QA (SA) Q4 Explanation
December 6, 2024
Explanation:
(32)
Given equation is log2 2(𝑙𝑜𝑔2 𝑥)^2 − 5 log2 𝑥 + 6 = 0
put log2 𝑥 = y, we get
log2 2^𝑦^2- 5y + 6 = 0
⇒ 𝑦^2∙ log22 − 5𝑦 + 6 = 0 [∵loga𝑎=1]
Solving above quadratic equation, we get,
y = 2 or 3
∴ log2 𝑥 = 2 or log2𝑥 = 3
= x = 2^2 or x = 2^3
= x = 4 or x = 8
∴ Roots of the given equation are 4 & 8.
∴ Product of the roots will be 32. Ans.