Let

n

be a positive even integer. Estimate

logn!!

based on the following formulas:\ Factorial formula:

n!=n*(n-1)*(n-2)dots2*1

\ Double factorial formula:

n!!=n*(n-2)*(n-4)dots4*2=2^((n)/(2))*((n)/(2))

!\ Logarithm formulas:

log(xy)=logx+logy,log((x)/(y))=logx-logy

, and

logx^(a)=a*logx

\ Stirling's formula:

logx!~~x*logx

Let n be a positive even integer. Estimate logn!! based on the following formulas: - Factorial formula: n!=n(n1)(n2).21 - Double factorial formula: n!!=n(n2)(n4)42=22n(2n) ! - Logarithm formulas: log(xy)=logx+logy,log(yx)=logxlogy, and logxa=alogx - Stirling's formula: logx!xlogx