Question:

<div class="solution"><p><strong>Key Idea:</strong> For <span class="math-inline">$\sin^{-1}(u)$</span> to be defined, <span class="math-inline">$-1\le u\le 1$</span>.</p><p><strong>Step 1:</strong> <span class="math-block">$$-1\le\log_2(x/3)\le 1$$</span></p><p><strong>Step 2:</strong> Convert to exponential: <span class="math-block">$$2^{-1}\le\frac{x}{3}\le 2^1 \implies \frac{3}{2}\le x\le 6$$</span></p><p><strong>Answer: (C) <span class="math-inline">$[3/2,\,6]$</span></strong></p><div class="trap-box"><strong>Trap:</strong> Forget to multiply by 3 across the full inequality, or confuse base-2 conversion.</div><div class="key-concept"><strong>Key Concept:</strong> Nested ITF domain — solve from outermost function inward</div></div>