Using array columns as arguments of a macro

Question

I am creating a table using array, and I want one of my columns to be used as the argument of xrightarrow as shown below. To make the code cleaner, I want to avoid having to write xrightarrow for each row of the table. I tried using the functionality of the array package to make the second column the argument of xrightarrow (my feeble attempts are commented out below). Is there any way to make this work, or do I need to repeat the xrightarrow for each row of the table?

\documentclass{article}
    \usepackage{amsmath}
    \usepackage{array}

\begin{document}

\[
    \begin{array}{l@{\qquad}c@{\qquad}l}
        Y = \alpha X^{\beta}
        & \xrightarrow{X' = \log(X) , Y' = \log(Y)}
        & Y' = \log(\alpha) + \beta X' \\
        Y = \alpha \exp(\beta X)
        & \xrightarrow{Y' = \log(Y)}
        & Y' = \log(\alpha) + \beta X
    \end{array}
\]

%\[
%   \begin{array}{l@{\qquad}>{\xrightarrow}c@{\qquad}l}
%       Y = \alpha X^{\beta}
%       & X' = \log(X) , Y' = \log(Y)
%       & Y' = \log(\alpha) + \beta X' \\
%       Y = \alpha \exp(\beta X)
%       & Y' = \log(Y)
%       & Y' = \log(\alpha) + \beta X
%   \end{array}
%\]
%
%\[
%   \begin{array}{l@{\qquad}>{\xrightarrow{}c<{}}@{\qquad}l}
%       Y = \alpha X^{\beta}
%       & X' = \log(X) , Y' = \log(Y)
%       & Y' = \log(\alpha) + \beta X' \\
%       Y = \alpha \exp(\beta X)
%       & Y' = \log(Y)
%       & Y' = \log(\alpha) + \beta X
%   \end{array}
%\]

\end{document}