Node on the ends of an arrow sign

Question

I have a plot where I have 2 arrows with nodes. For the red one I used \draw [<-,red,line width=0.6pt] (6,8) -- (30,8) node [right,black,draw=red,fill=white] {$\dfrac{a}{b}=\dfrac{3}{2}$}; command, which produced a left pointing arrow with the node on its right end. I used the command \draw [->,blue,line width=0.6pt] (0.6,8) -- (3,8) node [left,black,draw=blue,fill=white] {$\dfrac{a}{b}=\dfrac{5}{2}$}; for the blue one, but it didn't result in a right pointing arrow with the node on its left end. Can someone, please, explain it to me why it didn't work and how can I fix it? Below is the full code.

\documentclass{standalone}

\usepackage{amsmath,amssymb}
\usepackage{graphicx}% Include figure files
\usepackage{bm}
\usepackage[numbers,super,comma,sort&compress]{natbib}
\usepackage{tikz}
\usetikzlibrary{tikzmark,patterns}
\usetikzlibrary{arrows,arrows.meta,shapes.arrows}
\tikzset{>=latex}
\usepackage{pgfplots}
\usepackage{pgfplotstable}%fitting functions

\pgfplotsset{compat=newest}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
    xmode=log,
    width=8cm,
    height=6cm,
    axis line style={line width=0.6pt},
    x label style=
        {at={(ticklabel cs:0.5)},anchor=near ticklabel},
    xlabel={$x$},
    xmin=0.1,xmax=1000,
    xtick={0.1,1,10,100,1000},
    xtick align=inside,
    y label style=
        {at={(ticklabel cs:0.5)},anchor=near ticklabel},
    ylabel={$y$},
    ymin=0,ymax=10,
    ytick={0,2,...,10},
    ytick align=inside,
]

\addplot [red,line width=0.6pt,domain=0.1:10,samples=200] {3*x/2};
\addplot [blue,line width=0.6pt,domain=0.1:10,samples=200] {5*x/2};

\draw [<-,red,line width=0.6pt] (6,8) -- (30,8) node [right,black,draw=red,fill=white] {$\dfrac{a}{b}=\dfrac{3}{2}$};
\draw [->,blue,line width=0.6pt] (0.6,8) -- (3,8) node [left,black,draw=blue,fill=white] {$\dfrac{a}{b}=\dfrac{5}{2}$};

\end{axis}
\end{tikzpicture}

\end{document}