Are you sure you want \tracingall, You can be more specific in what you put out, eg
\documentclass{article}
\loggingoutput\scrollmode
\begin{document}
\sbox0{\parbox{2cm}{on two three four five six\[a=2\]seven}}
\typeout{my first box looks like this:}
\showbox0 \usebox0
\sbox0{\parbox{4cm}{on two three four five six\[a=2\]seven}}
\typeout{my second box looks like this:}
\showbox0 \usebox0
\end{document}
which produces
my first box looks like this:
> \box0=
\hbox(33.97223+28.97221)x56.9055
.\mathon
.\vbox(33.97223+28.97221)x56.9055
..\hbox(6.94444+0.0)x56.9055, glue set 0.5633
...\hbox(0.0+0.0)x0.0
...\OT1/cmr/m/n/10 o
...\OT1/cmr/m/n/10 n
...\glue 3.33333 plus 1.66666 minus 1.11111
...\OT1/cmr/m/n/10 t
and
my second box looks like this:
> \box0=
\hbox(27.97223+22.97221)x113.81102
.\mathon
.\vbox(27.97223+22.97221)x113.81102
..\hbox(6.94444+0.0)x113.81102, glue set 4.2553fil
...\hbox(0.0+0.0)x0.0
...\OT1/cmr/m/n/10 o
...\OT1/cmr/m/n/10 n
...\glue 3.33333 plus 1.66666 minus 1.11111
...\OT1/cmr/m/n/10 t