<p>If \(\log_{16}(\log_4(\log_3(\log_3 5))) = \frac{1}{2}\); find <i>x</i>.</p>
Step-by-Step Solution
Key Concept: Apply the definition of logarithm iteratively, working backwards from the outermost logarithm.
<p><strong>Solution:</strong> Working backwards from the outermost logarithm:</p><p>$\log_{16}(\log_4(\log_3(\log_3 5))) = \frac{1}{2}$</p><p>∴ $\log_4(\log_3(\log_3 5)) = 16^{1/2} = 4$</p><p>∴ $\log_3(\log_3 5) = 4^4 = 256$</p><p>∴ $\log_3 5 = 3^{256}$</p><p>∴ $x = 5$</p>
Correct Answer: 5