how to use Logitech Anywhere MX back/forward button on OSX Finder?

Solution 1:

In the Logitech Control Center, change the assigned action for Thumb Back Button and Thumb Forward Button to Keystrokes instead of Back and Forward.

For Thumb Back Button, set the keystroke to ⌘[ (Command-[) and for Thumb Forward Button, set it to ⌘] (Command-]).

(This keystroke combination can be seen in the Firefox Keyboard Shortcuts page (currently at Help > Keyboard Shortcuts), and in the Chrome Keyboard shortcuts page as well (Help > Keyboard shortcuts).