There is a formula to approximately calculate n! by Stirling:

N!≈√{2⋅π⋅N}⋅(÷{N}{e})^N

In logarithms, we get:

\ln N!=\ln √{2⋅π⋅N}+N⋅\ln N-N⋅\ln e
\ln N!=\ln √{2⋅π⋅N}+N⋅\ln N-N
\ln N!=÷{1}{2}⋅\ln 2⋅π⋅N+N⋅\ln N-N
\ln N!=÷{1}{2}⋅(\ln 2+\ln π+\ln N)+N⋅\ln N-N

For very big N, we approximately get:

\ln N!≈N⋅\ln N-N