Evaluate the following limit, if exists P \[ \lim _{x \rightarrow 1...

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Evaluate the following limit, if exists
P
\[
\lim _{x \rightarrow 1} \frac{(\ell n(1+x)-\ln 2)\left(3 \cdot 4^{x-1}-3 x\right)}{\left[(7+x)^{\frac{1}{3}}-(1+3 x)^{\frac{1}{2}}\right] \cdot \sin (x-1)}
\]
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