Discussion

Explanation:

Given, log₂[log₃(log₄a)] = log₃[log₄(log₂b)] = log₄[log₂(log₃c)] = 0

⇒ log₂[log₃(log₄a)] = 0
⇒ log₃(log₄a) = 2⁰ = 1
⇒ log₄a = 3¹ = 3
⇒ a = 4³ = 64

Also, log₃[log₄(log₂b)] = 0
⇒ log₄(log₂b) = 3⁰ = 1
⇒ log₂b = 4¹ = 4
⇒ b = 2⁴ = 16

Also, log₄[log₂(log₃c)] = 0
⇒ log₂(log₃c) = 4⁰ = 1
⇒ log₃c = 2¹ = 2
⇒ c = 3² = 9

∴ a + b + c = 64 + 16 + 9 = 89.

Hence, option (c).

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