How come this
(log(5/2)^4 ) / 2
equal this
2 log (-5/2)
????
=1/2 Log^4(5/2)
=1/2 x 0.39794^4
=0.01253835........etc.
I think you may have written your equation incorrectly...the parentheses are incorrect....and I do not know where the negative sign came from.....
log (( 5/2)^4) / 2 =
4log(5/2) / 2 =
2 log(5/2)
http://www.wolframalpha.com/input/?i=(log(5%2F2)%5E4+)+%2F+2&rawformassumption=%7B%22FunClash%22,+%22log%22%7D+-%3E+%7B%22Log10%22%7D
+37146 
