Discussion

Explanation:

f(x) = log7{ log3(log5(20x – x2 – 91 ))}

As log of negative numbers is not defined,

log3 (log5 (20x - x2 - 91)) > 0

∴ log5 (20x - x2 - 91)) > 30

∴ log5 (20x - x2 - 91) > 1

∴ 20x - x2 - 91 > 5

∴ 20x - x2 - 96 > 0

∴ x2 - 20x + 96 < 0

∴ (x - 12) (x - 8) < 0

∴ 8 < x < 12

Hence, option (b).

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