$\mathop {\lim }\limits_{x \to 1 } \frac{{\left( {\log \left( {1 + x} \right) - \log 2} \right)\left( {3 \cdot 4^{x - 1} - 3x} \right)}}{{\left( {{{\left( {7 + x} \right)}^{1/3}} - {{\left( {1 + 3x} \right)}^{1/2}}} \right)\sin \pi x}}$ ની કિંમત શોધો.

• A
  $\frac{9}{\pi }\left( {2\log 2 - 1} \right)$
• B
  $\frac{9}{{4\pi }}\left( {\log 4 - 1} \right)$
• C
  $\frac{9}{{2\pi }}\left( {\log 4 - \frac{1}{2}} \right)$
• D
  $\frac{2}{{3\pi }}\left( {2\log 2 - 1} \right)$