The product of the roots of the equation log22(log2x)2 - 5log2 x + 6 = 0
Explanation:
Here, let log2x = a
The given equation can be written as: a2 × log22 - 5a + 6 = 0 ⇒ a2 - 5a + 6 = 0 [log22 = 1] ⇒ a2 - 3a - 2a + 6 = 0 ⇒ a(a - 3) - 2(a - 3) = 0 ⇒ (a - 3)(a - 2) = 0 ⇒ a = 2 or 3
⇒ log2x = 2 or log2x = 3 ⇒ x = 22 or x = 23 ⇒ x = 4 or x = 8
∴ Required product of the roots = 4 × 8 = 32
Hence, 32.
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