#include<stdio.h>
#include<math.h>
int main()
{
int n;
scanf("%d",&n);
while(n--)
{
int m,i;
double s=0;
scanf("%d",&m);
for(i=1;i<=m;i++)
s=s+log10(double(i));
printf("%d\n",(int)s+1);
}
return 0;
}

法二：

#include<stdio.h>
#include<math.h>
#define p 3.14159265
#define e 2.71828182
int main()
{
int n;
scanf("%d",&n);
while(n--)
{
int m,i;
double s;
scanf("%d",&m);
s=log10(2*p*m)/2+m*log10(m/e);
printf("%d\n",(int)s+1);
}
return 0;
}