Discussion

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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