What do you want done with it?
Here's some simplifying, but without an actual question we don't know what kind of answer we're looing for.
120( ln(5x^(3/2)) + ln(3y) - ln(4 * (16z^5)^(1/2) ) )
120( ln(5) + ln(x^(3/2)) + ln(3) + lny - ln(4 * 4 * z^(5/2) ) )
120( ln(5) + (3/2) lnx + ln(3) + lny - ln(16z^(5/2)) )
120( ln(5) + (3/2) lnx + ln(3) + lny - ln(16) - ln(z^5/2) )
120( ln(5) + (3/2) lnx + ln(3) + lny - ln(16) - (5/2) lnz )
120 ln(5) + 180 lnx + 120 ln(3) + 120 lny - 120 ln(16) - 300 lnz
180 lnx + 120 lny - 300 lnz + 120 ln(5) + 120 ln(3) - 120 ln(16)
180 lnx + 120 lny - 300 lnz + 120(ln(5) + ln(3) - ln(16))
180 lnx + 120 lny - 300 lnz + 120 ln(5*3/16)
180 lnx + 120 lny - 300 lnz + 120 ln(15/16)
