Basic Mathematics & Logarithm
Logarithmic Functions
Grade 11

Question:

<p>log₂log₂(\(2^{4^{...^{3}}}\) with <i>n</i> times) is equal to</p>
<p>(a) 0</p>
<p>(b) 1</p>
<p>(c) <i>n</i></p>
<p>(d) −<i>n</i></p>

Step-by-Step Solution

Key Concept: Each application of log₂ reduces the height of the exponential tower by one level.
<p>For the tower of exponentials with <i>n</i> iterations, applying log₂ repeatedly <i>n</i> times reduces the exponent structure, yielding result <i>n</i>.</p>
Correct Answer: C

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