If log(9!) = 5.5598, what is the value of log(10!)? (show work)

Hi gyrocopter!!


I will use the following property:

log(a*b) = log(a) + log(b)

9! = 9*8*7*6*5*4*3*2*1 , 

then

log(9!) = log(9)+log(8)+...+log(1) = 5.5598


10! = 10*9*8*7*6*5*4*3*2*1 = 10*9! , 

then

log(10!) = log(10) + log(9!) = 
         = 1 + 5.5598 =
         = 6.5598


I hope this helps. Feel free to request for a clarification if it needed.

Regards.
livioflores-ga