How can I view the stdout / stderr from the bash login shell?

I'm trying to debug a strange issue with my ~/.bash_profile, and I'd like to be able to see if there are any errors / etc printed when it's run. Is there some log or such somewhere that contains the stdout and/or stderr of the login shell process? Thanks!

To debug a bash script you have several options, and some of these are even more effective than redirecting stdout/stderr.

Activate trace

You could add to your ~/.bash_profile (creating a trace only for specific parts of your script) with

set -x          # activate debugging from here
<commands>
set +x          # stop debugging from here

Also, set -v prints shell input lines as they are read, and set +v deactivates this. With this alone you will likely catch the problem.

Redirect trace

Use Bash Variable BASH_XTRACEFD

If set to an integer corresponding to a valid file descriptor, Bash will write the trace output generated when ‘set -x’ is enabled to that file descriptor. This allows tracing output to be separated from diagnostic and error messages. The file descriptor is closed when BASH_XTRACEFD is unset or assigned a new value. Unsetting BASH_XTRACEFD or assigning it the empty string causes the trace output to be sent to the standard error. Note that setting BASH_XTRACEFD to 2 (the standard error file descriptor) and then unsetting it will result in the standard error being closed.

So you would use

exec 5> ~/bash_profile_ouput.txt
BASH_XTRACEFD="5"
<commands>
unset BASH_XTRACEFD

Print line numbers

Use Bash Variable LINENO (and BASH_LINENO, BASH_SOURCE and/or FUNCNAME in more elaborate cases)

echo "Executing ${LINENO}"
<commands>

Redirect stdout/stderr

Combine command exec with redirection, and possibly tee. See answers here, which also include other methods/"tricks" than using exec.

Related:

1. https://stackoverflow.com/questions/44249890/pipe-bash-stdout-only-in-debug-mode
2. https://unix.stackexchange.com/questions/334382/find-out-what-scripts-are-being-run-by-bash-on-startup
3. https://unix.stackexchange.com/questions/155551/how-to-debug-a-bash-script

stdout and stderr will appear in the terminal everytime you do a login. You must log out and back in again for the changes in your profile to take effect. A further explanation of the use of ~/.bash_profile is provided here on Ask Ubuntu with a good answer

Tbh I didn't try myself, but I'm pretty sure standard output and error are the terminal it's running on, as soon as the process starts. You can check by putting a command such as echo "Hello world" in your .bash_profile...