$ Eq=prod_{k=1}^{K}(some-very-long-expression)^{z_{k}} $

$ log(Eq)=sum_{k=1}^{K}{z_{k}log(some-very-long-expression)} $

documentclass{article}
newcommandmymacro{mbox{(some-very-long-expression)}} % just for this example
begin{document}

begin{equation}
Eq = prod_{k=1}^{K} mymacro^{z_{k}}
end{equation}
followed by
begin{equation}
log(Eq) = sum_{k=1}^{K} z_{k} log mymacro
end{equation}

end{document}