You can put this solution on YOUR website! I finally tried this ON PAPER, and it was a difficult task with many opportunities for errors to lead to both or either confusion and wrong answers. I will NOT try to show all the steps by typing text.
Try working from the inside and go outward; and then to continue, you have some split exponents to deal with from level to level; so again start from inside and go outward again.
So far, not yet finished, I have this:
log((x^(5/2)y^(3/4)z^(3/8)))
Which becomes rendered as:
Hopefully that appears correctly; at least you can refer to the pure text form. You should have no further trouble continuing the necessary steps to finish.