documentclass[10pt,twoside,leqno,fleqn]{article}
usepackage{amsmath}

usepackage{enumitem}
usepackage{hyperref}
makeatletter
newcommand{leqnomode}{tagsleft@true}
newcommand{reqnomode}{tagsleft@false}
makeatother
begin{document}
reqnomode
begin{gather}
eqref{eq:Ix}= eqref{eq:I0}eqref{eq:e}^{-eqref{eq:mu} eqref{eq:x}}
end{gather}
%works but the parenthesis..
%begin{gather}
%ref{eq:Ix}= ref{eq:I0}ref{eq:e}^{-ref{eq:mu} ref{eq:x}}
%end{gather}
%! Missing endgroup inserted.

leqnomode
setlength{abovedisplayskip}{0pt}
setlength{belowdisplayskip}{0pt}
begin{itemize}[label=]
    leftskip=1cm
    item begin{equation}
    tag*{$I_{(x)}$}label{eq:Ix} textnormal{: text1}
end{equation}
    item begin{equation}
    tag*{$I_0$}label{eq:I0} textnormal{: text2 }
end{equation}
    item begin{equation}
    tag*{$e$}label{eq:e} textnormal{: text3}
end{equation}
    item begin{equation}
    tag*{$mu$}label{eq:mu} textnormal{: text4}
end{equation}
    item begin{equation}
    tag*{$x$}label{eq:x} textnormal{: text5}
end{equation}
end{itemize}
end{document}

documentclass[10pt,twoside,leqno,fleqn]{article}
usepackage{amsmath}

usepackage{enumitem}
usepackage{hyperref}
makeatletter
newcommand{leqnomode}{tagsleft@true}
newcommand{reqnomode}{tagsleft@false}
makeatother


newcommand{mref}[1]{textup{ref{#1}}}

begin{document}
reqnomode

begin{align}
    mref{eq:Ix}= mref{eq:I0}mref{eq:e}^{-mref{eq:mu} mref{eq:x}}
end{align}

%works but the parenthesis..
begin{gather}
    mref{eq:Ix}= mref{eq:I0}mref{eq:e}^{-mref{eq:mu} mref{eq:x}}
end{gather}
%! Missing endgroup inserted.

leqnomode
setlength{abovedisplayskip}{0pt}
setlength{belowdisplayskip}{0pt}
begin{itemize}[label=]
    leftskip=1cm
    item begin{equation}
    tag*{$I_{(x)}$}label{eq:Ix}textnormal{: text1}
end{equation}
    item begin{equation}
    tag*{$I_0$}label{eq:I0} textnormal{: text2 }
end{equation}
    item begin{equation}
    tag*{$e$}label{eq:e} textnormal{: text3}
end{equation}
    item begin{equation}
    tag*{$mu$}label{eq:mu} textnormal{: text4}
end{equation}
    item begin{equation}
    tag*{$x$}label{eq:x} textnormal{: text5}
end{equation}
end{itemize}



end{document}