Question:

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