Note that 0.5 log(1.5 W) + 0.5 log(0.6 W) = 0.5 log(1.5) + 0.5 log(0.6) + log(W) I wrote it that way to make the comparison with the alternative log(W) more ob

Note that 0.5 log(1.5 W) + 0.5 log(0.6 W) = 0.5 log(1.5) + 0.5 log(0.6) + log(W) I wrote it that way to make the comparison with the alternative log(W) more obvious.