Does log(decimal!) Exist?

$A=\lim _{ x\rightarrow 1 }{ \frac { \log _{ e }{ \left( \left( 10.5x \right) ! \right) -\log _{ e }{ \left( \left( 10.5 \right) ! \right) } } }{ x-1 } } \\ =\lim _{ x\rightarrow 1 }{ \frac { \log _{ e }{ \left( \Gamma \left( 10.5x+1 \right) \right) -\log _{ e }{ \left( \left( 10.5 \right) ! \right) } } }{ x-1 } } \\ Using\quad L'hospital's\quad rule,\\ A=10.5\psi (11.5)\\ \quad =10.5\left\{ -\gamma -2ln2+\sum _{ k=1 }^{ 11 }{ \frac { 2 }{ 2k-1 } } \right\} \\ \quad =25.181\\ \psi \quad is\quad used\quad to\quad represent\quad digamma\quad function.\\ \gamma \quad is\quad Euler-Mashcheroni\quad constant.$