Basic Mathematics & Logarithm
Logarithmic Equations
Grade 11

Question:

<p>The value of log₄[log₂{log₂(log₃ 81)}] is equal to</p>
<p>(a) −1</p>
<p>(b) 0</p>
<p>(c) 1</p>
<p>(d) 2</p>

Step-by-Step Solution

Key Concept: Evaluate nested logarithms from the innermost function outward, using the fact that log_a(a^n) = n.
<p><strong>Step 1:</strong> Evaluate from innermost: log₃ 81 = log₃ 3⁴ = 4</p><p><strong>Step 2:</strong> log₂ 4 = log₂ 2² = 2</p><p><strong>Step 3:</strong> log₂ 2 = 1</p><p><strong>Step 4:</strong> log₄ 1 = 0</p><p>∴ Answer is (b) 0.</p>
Correct Answer: B

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