Question Number 185701 by Khalmohmmad last updated on 26/Jan/23
$$\mathrm{1000}! \\ $$
Commented by Rasheed.Sindhi last updated on 26/Jan/23
$$\mathrm{999}!×\mathrm{1000} \\ $$
Commented by Frix last updated on 26/Jan/23
$${x}!\approx\frac{{x}^{{x}} }{\mathrm{e}^{{x}} }\sqrt{\mathrm{2}\pi{x}} \\ $$$$\mathrm{log}\:{x}\:=\mathrm{log}_{\mathrm{10}} \:{x}\: \\ $$$$\mathrm{log}\:{x}!\:\approx\:\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{log}\:{x}\:−{x}\mathrm{log}\:\mathrm{e}\:+\frac{\mathrm{log}\:\pi\:+\mathrm{log}\:\mathrm{2}}{\mathrm{2}} \\ $$$$\mathrm{1000}!\:\approx\:\mathrm{1000}.\mathrm{5}×\mathrm{3}\:−\mathrm{1000log}\:\mathrm{e} \\ $$$$\mathrm{1000}!\:\approx\:\mathrm{1}.\mathrm{56}×\mathrm{10}^{\mathrm{3436}} \\ $$