Verified answer

lnx - (lny - lnz) =

lnx - lny + lnz =

ln(x/y) + lnz =

ln(xz/y)

ln x - (ln y - ln z) = ln x - ln y + ln z = ln (x z/y)

ln x - (ln y - ln z) = ln x - ln(y/z) = ln(x/(y/z)) = ln(xz/y)

ln(x) - (ln(y) - ln(z)) =>

ln(x) - ln(y) + ln(z) =>

ln(x * z / y)

Log[ (x z)/y]