½log10(25/4)-2log10(4/5)+log10(320/125)
The rules of logs are:
a.log(x) =log(x^a) ----------------- I
-log(x) = log(1/x) ------------------ II
log(a) + log(b) = log(ab) -------- III
using I, ½log(25/4) = log([25/4]^½) = log(5/2)
using I & II, -2log(4/5) = -log([4/5]^2) = -log(16/25) = log(25/16)
Adding together these logs, using III,
½log10(25/4)-2log10(4/5)+log10(320/125) = log(5/2) + log(25/16) + log(320/125) = log(5/2*25/16*320/125) = log(10) = log10(10) = 1
Answer: 1