How do you use the properties of logarithms to expand log_10((xy^4)/z^3)?

##log x +4log y -3log z##
##log_10x=logx## since base 10 is assumed.
##log((xy^4)/z^3)##
##log(a/b)=loga-logb##
##log xy^4-logz^3##
##logab=loga+logb##
##logx+logy^4-logz^3##
##loga^b=bloga##
##logx+4logy-3logz##