It look like duplicate of this Save the console.log in Chrome to a file ,but Accepted answer doesn't seem to work anymore and rest are third party plugin. Also question is very old. Asking for any update.
I tried using above solution, but console-debug log doesn't print console.log
I am using chromium 40 on IMX6Q Board with Linux and not allowed to install any extension.
There is native support to do this. Right click console area and choose "Save as".
Tested with Chrome Version 43.0.2357.130 m