Solution set of inequality <span class="math-tex">\(\log_3 (x + 2)(x + 4) + \log_{\frac 1 3} (x + 2) < \frac 1 2 \log_\sqrt 3 7\)</span> is
Domain: \(x + 2 > 0\), so \(x > -2\) (then \(x + 4 > 0\) too).
\(\log_3[(x+2)(x+4)] - \log_3(x+2) = \log_3(x+4)\)
RHS: \(\frac{1}{2}\log_{\sqrt{3}}7 = \frac{1}{2} \cdot 2\log_3 7 = \log_3 7\)
\(\log_3(x+4) < \log_3 7 \Rightarrow x + 4 < 7 \Rightarrow x < 3\)
Solution: \((-2, 3)\)
Answer: (B)
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