Discussion

Explanation:

log4 log4 4a - b = 2log4 a-b + 1

∴ log4 (a - b) log4 4 = 2log4 a-b + 1

∴ log4 (a - b) = 2log4 a-b + 1

∴ log4 (a - b) = 2log4 a-b2 + 1

∴ log4 a-ba-b2 = 1

∴ a-ba+b-2ab = 4

∴ a - b = 4a + 4b - 8ab

∴ 8ab = 3a + 5b

∴ 8 = 3ab + 5ba

Let ab = x

∴ 8 = 3x + 5x

∴ 8x = 3x2 + 5

∴ 3x2 - 8x + 5 = 0

∴ 3x2 – 3x – 5x + 5 = 0

∴ 3x(x – 1) – 5(x – 1) = 0

∴(3x – 5)(x – 1) = 0

∴ x = 53 or x = 1

But x ≠ 1 as a ≠ b

∴ x ≠ 5/3

∴ ab = 53

Hence, option (c).

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