Solving an inequality $BIs there a way to solve $B<n!$ where $B$ is some very large real number (suppose for example $B=10^{17}$) without a calculator or gamma function?
At the very least, to find the nearest integer for $n$ to make the inequality true?

With a log table, you could do it by hand :
Compute $\ln(B)=17 \ln(10)$
Then you just have to sum the log of the numbers :
$$\ln(n!) = \sum_{k=2}^n \ln(k)$$
