Limit-ed

Calculus Level 3

\[\large \lim_{x \to 1} \dfrac { (\ln(1+x) - \ln2) (3\cdot 4^{x-1} - 3x) } { \left((7+x)^\frac 13 - (1+3x)^\frac 12 \right) \sin(x-1) } =\, ? \]

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