Existe um comando para isso:
which firefox
/usr/bin/firefox
Na página man de which
:
HICH (1) Manual de Comandos Gerais WHICH (1)
NAME
which - locate a command
SYNOPSIS
which [-a] filename ...
DESCRIPTION
which returns the pathnames of the files (or links) which would be exe‐
cuted in the current environment, had its arguments been given as com‐
mands in a strictly POSIX-conformant shell. It does this by searching
the PATH for executable files matching the names of the arguments. It
does not follow symbolic links.